Why is my MacBook Pro so hot?

Sounds like a failed heat sink to me. They usually leak at the crimped ends. It leaves a small greasy looking residue. Since your’s is located on the bottom side of the logic board, it is harder to get to. The spot may be harder to detect . I’d also replace the thermal paste when doing a replacement.See step #22 of this guide:

Sostituzione dissipatore MacBook Pro Unibody 13" metà 2012

Here’s the part:

MacBook Pro 13" Unibody (Mid 2012) Heat Sink

I’ve also been very pleased with these Quicksand Rubberized Matt Hard Case Cover Cut-out for MacBook Pro, I like the black and wine red ones: https://picclick.com/Quicksand-Rubberize...