The expression “to turn the heat on” seems originally to have been underworld slang, probably a rough interpretation of “to be grilled” in its figurative sense.
It means, to be subjected to a severe cross-examination, as by police officers in grilling a suspected criminal; but of course in ordinary use a youngster will say that his dad turned the heat on when asking how the fender of the car got dented.
The expression is quite recent.
