MacBook Pro is getting to ~200 F from just watching Youtube

"Service Battery" indicates that macOS has detected a hardware fault with the battery so you should have Apple or an AASP examine the laptop.

As for the heating issue Google Chrome is notorious for causing CPU & memory issues which also means it can make a system run hot. To look for other possible software issues contributing to the higher temperatures run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.

macOS will allow a laptop to get to 80C to 90C sometimes before the fan speed increases (doing anything on a CPU core will cause the temp to spike even if just for a second). If the CPU is being heavily utilized, then it is not uncommon to see CPU temps at 90C (once it hits 100C the CPU will become throttled if the fans are running at maximum speed). In most cases these Macs will attempt to keep the temps between 60C to 95C depending on the workload. In the future please post temperature in Celcius since benchmark & product reviews only reference temps in Celcius.

See if your laptop qualifies for this free battery repair program:

https://support.apple.com/13inch-macbookpro-battery-replacement

FYI, here is the current list of the publicly acknowledged free repair programs for various Apple products (some products have multiple programs):

https://support.apple.com/service-programs

Hi there, Razuto22! Thanks for reaching out to Apple Support Communities. 

After reviewing your post, it sounds like you are experiencing a few issues with your MacBook Pro. We definitely understand that this can be a concern and we'd love to help. We have a few articles we suggest reviewing that may be of help with these issues:

• Keep your Mac notebook within acceptable operating temperatures
• About fans and fan noise in your Apple product
• Get help with your Mac notebook battery
• Use Apple Diagnostics to test your Mac

Please let us know if you have follow-up questions about these issues after you do some testing and make suggested changes from the articles. We are here to help. Have a great day!

Razuto22 wrote:

Thanks for the info! I will have to go in and get the battery checked out. I will download EtreCheck as well and will run it when high temps occur again.

No need to wait for the issue to occur again before running EtreCheck.

I didn't realize that Celcius was the benchmark – that's good to know from now on!

This is the only time I use Celcius myself.