I use Chrome and a few small other programs, nothing with high load,
First, Chrome is not light usage. If is very resource hungry and can be a source of heating. So can useless add-ons like anti-virus and so-called "cleaning" apps.
13-inch Macbook Pros of that vintage have the least cooling capacity of the series. They have but one cooling fan and no side vents for cool air intake. All the airflow is through the hinge ara and the keyboard. If either is blocked, temps will rise dramatically and the fans will speed up in reaction to the heating.
Much of that usage/position info is covered in this Apple article:
Keep your Mac laptop within acceptable operating temperatures - Apple Support
Even with more friendly browsers, I am finding more web sites that continue to update in a background tab if left open.
So can apps. Two days ago I had MS Word and Safari running on my Macbook Pro and the temps were where they always run, about 45°C. At that temp the fans are happy at their base speed of 2000 rpm. Then I launched Google Earth to check a location and,within three minutes, the fans spun up to almost 5000 rpm and the temp was at 71°C. As soon as I quit Google Earth, temps were back to normal in minutes.
Heating can be from software, positioning of the computer, or both.
