Can Heat Transfer Through Conduction Occur at Relativistic Speeds?

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Josh0768
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Are there any known instances of heat transfer via conduction or convection happening at relativistic speeds? Is this even possible or is there a non-relativistic limit to how fast heat can transfer in these ways, like how sound can only move so fast?
 
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Heat transfer from radiation happens at the speed of light. What other speed would it happen at?
 
Vanadium 50 said:
Heat transfer from radiation happens at the speed of light. What other speed would it happen at?
I asked about heat transfer from conduction.