Thermal radiation is in fact emitted from the nucleus of atoms; all matter emits black body radiation. The reason hot things generally aren't considered radioactive is because that would pull literally all matter into the discussion.

But that wasn't the point being made here. The point being made with the hot spoon example is that EM radiation doesn't make other things radioactive (except insofar as it heats things up). This is equally true of gamma radiation as thermal radiation. Thermal radiation and gamma radiation can both cause harm directly, but neither will make other things radioactive.

That's why it's completely safe to eat food that was sterilized with gamma radiation intense enough to kill you outright.