The good doctor is probably right. On thinking about it, I realised that I didn't really know what heat is, so turned to wikipedia
"In physics and chemistry, especially in thermodynamics, heat refers to a process of transfer of energy between a system and its surroundings other than by work or transfer of matter.[1][2][3][4][5][6] It is measured as the quantity of energy that the process transferred. Familiar examples often involve the spontaneous transfer of energy as heat from a body at a higher temperature to an adjacent one one at a lower temperature, narrowing their temperature difference. The transfer can occur by the mechanisms of conduction[7] and radiation,[8] and in a more complicated way[9] called convective circulation."
But in the colloquial context of the original question I think that "heat" means "thermal energy", and then it is not unreasonable to talk about that flowing from one place to another.