At the risk of oversimplifying things, when your MBP is charging it needs to receive enough power from the AC outlet in order to charge the battery. However, when charging is complete and if the MBP is still connected to AC power, the charging process effectively goes into a float phase where it just keeps your battery charged and does not require the same amount of power coming through. So, it makes perfect sense that while charging there will be more heat as compared to while it's floating (for want of a better word).
If the heat while charging seems excessive to you (or you're just concerned about it), you can reset the System Management Controller (SMC). To do this:
- Shut down your MBP
- Keep the MagSafe adapter (power cable) plugged in.
- Press at the same time shiftoptioncontrol (on the left side of the built-in keyboard) and the power button
- Let go
- Turn your computer back on with the power button.
After doing this, use your computer for a while (incl. Google Chrome) to see if there is a change in the behaviour.
If you still have concerns about when Google Chrome is being used, you can change the hardware acceleration setting within Chrome. To do this:
- Launch Google Chrome
- Go to Chrome > Preferences (or just press the command, keyboard shortcut
- At the bottom of the page, click on Show advanced settings...
- Look for the System subheading in the new settings that appear
- Uncheck the Use hardware acceleration when available option
- Restart Google Chrome
Let us know how you go.