Take a piece of steel bar, 30 cms long x 1cm in diameter will do. Heat one end of it with a blowlamp as quickly as you can until it is bright cherry red. The end you are holding will barely become warm. Then plunge the hot end into around 10 cms of cold water. The cold end will almost instantly quickly get hot enough to burn your hand. No physics - and no tables of thermal conductivity - can explain that except for it being heat transport by bulk phonons moving through the lattice.
This can be done with a Kanthal resistor wire too.
If you suddenly cool one half of the glowing wire with water, the other half will start getting hotter.
Alternatively, if from room temperature conditions one half of the wire is kept cool with water, the other will also similarly heat up more with the same amount of input power into the wire.
I thought it might have to do with heat having one escape path (radiation) removed, therefore being forced to flow elsewhere.