In addition to what jksoegaard has stated in their answer, there are a couple of things you should do that may help in the short-term until you can replace your battery.
1. Reset the SMC
For starters, I would reset the System Management Controller (SMC) as that is key to your MBP's power management. To reset the SMC on your model MBP, follow these steps:
- Fully shut down your MBP
- Press and hold the Shift-Control-Option keys on the left side of your built-in keyboard while also pressing the power button and keep them all down for at least 10 seconds
- Let go of all keys and the power button
- Switch on your MBP
2. Disable hardware acceleration on Google Chrome
Disabling hardware acceleration on Google Chrome will reduce the power demands on your MBP. To do this:
- Go to Chrome > Preferences
- Scroll down to the bottom
- Click on Advanced
- Scroll down to the System heading
- Disable the Use hardware acceleration when available option
A final word
The above steps will not change the fact that you need to replace your battery. While jksoegaard is correct that The source of the heating up might also be something else entirely, it is highly likely the battery situation is at least contributing to this, if not the only cause.
As your MBP heats up the SMC will kick in to ensure that your MBP is protected from damage, so the SMC will do things like slow down your CPU, increasing your fan speeds, etc. Resetting the SMC may help in this, but replacing your battery will have a big impact.