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:

MacBook Pro (13 Zoll, Mitte 2012, Unibody) Kühlkörper Austausch

Here’s the part:

MacBook Pro 13" Unibody (Mid 2012) Heat Sink

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