Q: Fan working all time

A fan does run all the time though usually so low you don't know it. But if it starts to run at a high speed so as to be heard, the first thing to try is a SMC reset. With mag safe connected and macbook air off, hold down the Command/Option/Shift keys and power button for 10 seconds. If when you reboot you still have the problem. Then you may have some run away apps that are causing the fan to run because of heat.https://support.apple.com/en-us/HT203184

Did you perform the SMC reset as my ginger suggested? The instructions are below.

Power or other problems related to unexpected system sleep, shutdown, lights or fans call for an SMC reset. Read all the steps.

Before Resetting the SMC

Try each of the following steps in this order before you reset the SMC. Test the issue after completing each troubleshooting step to determine if the issue still occurs.

1. Press Command + Option + Escape to force quit any application that is not responding.
2. Put your Mac to sleep by choosing the Apple () menu from the upper-left menu bar and then choosing Sleep. Wake the computer after it has gone to sleep.
3. Restart your Mac by choosing the Apple () menu from the upper-left menu bar and then choosing Restart.
4. Shut down your Mac by choosing the Apple () menu from the upper-left menu bar and then choosing Shut Down.

Resetting the SMC on portables with a battery you should not remove on your own

1. Shut down the computer.
2. Plug in the MagSafe power adapter to a power source, connecting it to the Mac if it's not already connected.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time. The power adapter indicator light may cycle off / on once.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.

Hi Pablo, Yosemite offers another way to identify any software responsible for excessive energy consumption. Use Activity Monitor again, but select the CPU tab, and select the "Energy Impact" column to show relative energy usage by process in descending order.

See the following screenshot, which is for Mavericks, but Yosemite is similar:

Describe the processes consuming the greatest amount of energy, or attach a screenshot like the above.

You can also click the battery icon in your Mac's menu bar to reveal significant energy hogs (UPS is shown below):

If one or more processes are burdening the CPU, it will become evident.

Determine if a defective temperature sensor may be responsible. To do that Apple Hardware Test or use Apple Diagnostics. Apple Hardware Test is for Macs produced prior to June, 2013. Later Macs use Apple Diagnostics.

Mac notebooks: Apple Hardware Test may report "HDD" alert

If none of the above reveals anything useful, write back for more suggestions.

Pablo, Google Chrome stands out as consuming excessive energy. Chrome installs many system modifications and is notorious for causing poor performance on Macs. Apps that consume excessive energy will cause excessive heat generation, which will require the exhaust fan to run faster than they would otherwise.

The screenshot I posted is very typical. the "Energy Impact" values have no units of measurement, but I have never seen anything approach what Chrome is using in yours.

Here is a more recent one. It's from an iMac, but it is running Yosemite. The "Energy Impact" values are representative of what I typically observe, even on a MacBook like yours:

To determine if Google Chrome is responsible, it's not enough to simply stop using it. You have to uninstall Chrome completely, according to its instructions.

If that does not resolve the problem, you can always install Chrome again.

You do not have the mag safe power connector ,so you have not done the SMC reset? Have you check the vent in the back to see if it is clogged or dirty?You might try doing the SMC reset without the power cord.