Are there any materials that don't emit infrared when heated?

No. Because then the Stefan-Boltzman's law has to be wrong which describes how temperature of a body is related to the electromagnetic radiation emission (like infrared) from it. read more

What they should emit depends on their bonding structure and in some case, it is used as a marker for indicating the presence of those material. So it is possible to have a material will not emit some wavelength of infrared significantly but other material when heated would emits that infra-red significantly. read more

You can use the same materials to reflect infra-red as you would use for visible light, i.e polished metals or metallic films. read more