I have read this question which seems to ask an identical question, but I'm not sure - it had far too many words I don't understand, let alone the equations. Perhaps someone can answer with a heat-for-dummies answer.
I understand that given thermal conductivity, and thermal mass, it takes a while for heat applied to one end of a material to make the other side rise in temperature. Like for a heat sink for electronics, with the component dissipating a constant power, and the ambient temperature staying constant, a thermal gradient will develop until it reaches an equilibrium, where the power dissipated by the electronic component equals the power dissipated by the heat sink to the ambient environment.
But my question is: say the heat sink is exactly at ambient temperature. And say the electronic component instantly starts dissipating to the heatsink a given power. How long would it take for the heatsink to start dissipating even the smallest amount of power to the environment? My guess is it would be equal to the speed of the molecules' vibrations that is otherwise known as heat.
Or perhaps at the speed of light, since thermal radiation would penetrate the material, even if it is very, very little.
I hope this makes sense?