It's linear to surface area, but 4th power to temperature.

Also worth noting that if computing power scales with volume then surface area (and thus radiation) scales like p^2/3. In other words, for a fixed geometry, the required heat dissipation per unit area goes like p^1/3. This is why smaller things can just dissipate heat from their surface, whereas larger things require active cooling.

I'm not a space engineer but I'd imagine that smaller satellites can make due with a lot of passive cooling on the exterior of the housing, whereas a shopping-mall sized computer in space would will require a lot of extra plumbing.

Thanks for the correction. Last time I looked at it was in 2nd year Thermodynamics in 1985.