*Probably* it's a defective TPRV.
But original poster noted that the water "seemed hotter than normal the
night before", from the description it does not sound like the TPRV is
"leaking", it sounds like it's open - which means *some* sort of event
opened it - from the post it does not sound like it was opened by the
owner (for example, for testing).
All of which is enough to red flag it for me as a "Turn it off, and
call the plumber" issue, at least if you want to be conservative and
err on the side of safety.
For readers with a high speed connection, this is IMO sorta'
Something along these lines happens around 50 times a year in the US.
Paragon Home inspection, LLC