Is it true it's not good to update to the latest OS X?

Those techs didn't know what they were talking about! Period!

Your year and model iMac can run the latest macOS Sierra just fine.

The only caveat is that it may not run as well with a minimum of RAM.

Newer Mac OS versions like a base minimum of 8 GBs of RAM, now.

Your year and model iMac can take, at least. 16 GBs of RAM and if it is an i5 or i7 CPU, that 2011 iMac model can take up to 32 GBs of RAM.

You MUST use THE EXACT RAM that your model iMac is spec'd for.

Correct and reliable Mac RAM can ONLY be purchased from online Mac RAM sources Crucial memory (crucial .com) or OWC, aka, Other World Computing (macsales.com).

When buying RAM for Macs from Crucial memory, purchase ONLY directly from the Crucial memory website. NOT from some other online source.

Good Luck!

Upgrading is usually safe although I personally, never upgrade until the 3rd update, and if things still invite criticism, I wait further.

In your case the machine may not be suitable for further upgrades and that is not unusual but I have read of examples running Sierra. The statement about old macs could be a sales ploy.

If you were not having issues running Sierra before the repair, why

would you think it is "unsafe" now?

As far as the "can't run it" comment, Apple wouldn't allow you to install

it if that were the case. I have Sierra running just fine on 2010 MacMini

and 2011 MacMini which are far less capable machines than yours.

8 GBs of RAM is really the base minimum just to run macOS Sierra.

You wiill find that this amount won't be sufficient for serious gameplay.

As far as the installation of your hard drive goes, it sound like the techs that installed your hard drive didn't install an Apple approved hard drive that needs the use of an additonal temp sensor that controls the speed of the fans.

It sounds like these tech really have no idea of what they were doing.

Apple uses special hard drives that have a place to install a special temperature sensor to the drive that regulates the fans. The techs either just installed an Apple approved new hard drive and forgot to reconnect the temp sensor OR they just installed any new hard drive they had on hand that has NO support for the needed temp sensor!

You can either bring your iMac back to them and tell them the problem with your internal fans are running at maximum when they weren't doing this before and ask them if they forgot to reinstall the temp sensor to the drive.

OR

You can run a software fans control to control the speed of your Macs internal fans manually.

There are two software fans control software for Macs that I am aware of.

SMC Fan Control

https://www.eidac.de/

Macs Fan Control

https://www.crystalidea.com/macs-fan-control

As far as installing RAM is concerned, RAM is relatively easy to install by new and novice users.

RAM is NOT hard to install.

Here is the proper RAM specs your iMac needs.

https://eshop.macsales.com/shop/memory/iMac/2011/DDR3_21.5_27

Here's how to install RAM into your 2011 iMac.

https://eshop.macsales.com/installvideos/imac_mid_2011_mem/

Good Luck!

You really need to do something about the internal fans running at full speed!

You'll end up burning up the fans' motors, in time, which will lead to premature internal heat failure of components and, eventually, sooner than later, fry your Mac!

You either need to bring your Mac into the repair shop and have the repair techs look at this again to see why the fans are running at full speed (I suspect the missing or disconnected temp sensor cable) OR you need to install one of the software fans controls that I provided links to.

The fans in your Mac should NOT be blaring at full speed inside of your Mac.

Eventually, sooner than later, you'll end up burning up the fan motors.

You really need to deal with this issue!

Yep.

Knew it!

They installed a new hard drive that can't use the special temp sensor that automatically controls the Mac's internal fans.

In your location, the repair place probably has no access to Apple approved hard drives that are compatible with the temp sensor.

Hitachi drives are, generally, pretty reliable drives, but without the connection for the temp sensor, YOU WILL NEED TO INSTALL a software fans control.

The easiest fans control software to is SMC fan control, but you have to set the fans to a static speed that isn't too slow to cause overheating, but NOT too fast to allow the internal fans to act like an internal vaccuum sucking in excessive outside dust, dirt and lint.

There are two software system monitors you can install.

Either iStat Menus

https://bjango.com/mac/istatmenus/

OR

iStat Mini

https://bjango.com/mac/istatmini/

To monitor a lot of different system things including your Macs internal fans.

YOU NEED TO INSTALL A MANUAL FANS SOFTWARE CONTROL!

For you son's gaming,

Macs Fan Control allows, I think, for multiple fans settings for different uses. Not sure, read the description on this control

SMC Fans Control only has one set of control, only. So, you will have to ramp up the fan speeds higher for your son's gaming habits.

But You need to get control of your Macs's internal fans. Period! No more arguing about it!

I use SMC Fans Control, but I am the only user and I don't game too much so, I am not sure of the fan settings needed to comfortable run the fan RPMs for gaming.

I run my fans at a speed that keeps most, but NOT every component run at slightly over 100° F and cooler, if posdible.

The Mac's power supply and GPU run the hottest! It's important to not let the GPU get very hot!

Any GPU temps into the 150°-160° F or higher is NOT good for the GPU.

I try to get my GPU to run lower than 130° F and go no higher than 140° F

Most times, in cooler weather, I can get my GPU to run in the middle to high 120°F range.

Good Luck to You!

I don't know why your Apple Authorised service center couldn't get an Apple approved hard drive.

Like I stated, maybe in your location in the world, maybe getting the special Apple hard drives from Apple or Apple sourced approved hard drives are difficult to get???

I gave you the option of bringing your Mac back to the service center and just telling them that the fans are running more and louder and see if they can identify the hard drive/temp sensor issue on their own.

Don't give them any hints. See if they find this issue, first.

If you want to complain directly to Apple about the service you got from your Apple authorised service center, you can contact Apple, directly, in Cupertino, California U.S.A at this phone number.

Maybe the shop Apple told you to use was the one you should have used.

1-800-MYAPPLE.

Not sure who you would need to talk with.

Hopefully, Apple can assist you over the phone.

Good Luck to You!

Not sure where you live/reside in the world, but there is one supplier of Apple approved hard drives and the needed temp sensor here.

https://eshop.macsales.com/shop/internal_storage/hard_drives_and_SSD?_ga=2.15129 0489.1748168253.1495567894-274293733.1478680016

You can call them to learn more about these internal drives and Mac compatibility. They, also sell a new temp sensor cable.

1-800-275-4576 OR 1-815-338-8685

Not sure how much it would cost you to get an Apple approved/compatible internal drive from the U.S., but OWC Macsales does do international shipping.

I would just go back to your AASP, first and see if they can straighten out the issue with the fans.

See what THEY tell you!

Out of curiosity, since you had to replace the internal drive, why didn't you have a 500 GBs or a 1 TB SSD inside of your Mac instead?

SSDs are much, MUCH faster than any mechanical spinning hard drives?

I am running my older iMac from an external FW800 SSD and I can't believe the difference in performance and responsiveness of my iMac.

I don't have any clues about any of that!

If you want to persue this with another AASP, that's your decision.

The easy and less-hassle free solution is just install the software fan controller and system monitor and learn how to use them and maybe spare yourself additional headaches/issues.

I hear you about calling Apple directly, but this is REALLY the only way to let Apple know that you weren't happy with your Mac repair experience.