Question

Is there material that heat moves through in only one direction?

Answer 1

Yes.

Explanation:

Technically one dimensional material allows heat to flow in one direction form high temperature to low temperature. Or you can channel the heat to flow in one direction by insulating surface(s) of the material exposed to the direction(s) you don't want heat to flow into, like a rod with its curved surface insulated.

Some bulk (3D) materials allow heat to flow favorably in one direction over others. So it is possible to have one dominant heat flow direction.

If you want heat to flow only in direction but can not reverse its flow in the opposite direction, acting like a thermal diode, such a material also exists.