A metal piece is heated to T₁ K. The temperature of the surroundings is T₂ K. The heat in the surroundings due to radiation is proportional to 

 E = $\sigma tA(T^4-T^4)$  STEFAN BOLTZMANS LAW

The metal piece emits heat ${\mathrm{\sigma T}}_1^4$ while it absorbs heat ${\mathrm{\sigma T}}_2^4$ from surroundings. Hence heat in the surroundings due to radiation is proportional to $\left({\mathrm{T}}_1^4-{\mathrm{T}}_2^4\right)$.