There are electrolytic capacitors near where he was heating, and the capacitance of electrolytics can have a strong temperature dependence. He probably managed to heat one of the electrolytic capacitors, which happened to change its capacitance in the correct direction to make the circuit work.
Chances are the monitor would work reliably if all the electrolytic capacitors were replaced.
Edit:
I'm guessing the problem is C208. Section 10 of the LDO data sheet, linked in the article, talks about how stability is dependent on the output capacitor (C208). C208 has probably dried out, reducing its capacitance and making the LDO unstable. Heating was enough to make the circuit stable (for a while).
Further edit:
Predating my comment, "Gordonjcp" also called out C208.