Variable thermoconducting alloy?

Is there an alloy with a variable rate of thermoconductivity? I’d imagine an engine made out of such a metal would have interesting cooling properties.
At startup, the cylinders would be cold, and thus insulating. As the engine warmed up, the metal becomes less insulating and more conducting, drawing excess heat away from the combustion chamber.

I found hits on semiconductors…for electrical conductivity, not thermal conductivity.

Generally, materials have thermal conductivities that depend on temperature, though not usually by much. Is the point of your idea that having insulative cylinders would make the engine run better at first, until the cylinder walls were hot and needed to export heat? Another way to accomplish this is to have most of the heat transfer through the engine block performed by coolant flowing through passageways, and then control the heat transfer rate by controlling the flow – and this is what is actually done in most engines. Yet another way would be to make dry sleeves (cylinder liners that are pressed into the block)with a greater CTE than the block so that they retract and don’t couple to the block at low temperature.