I'm trying to write a very, very simple heat flow simulation program. The idea is an environment space is a grid, with each grid space identical in respect to all other grid spaces (I'm calling a grid space an "element") except temperature. So, they are physically the same except temperature differences. I have found a formula for power output from a hot object in a cool environment: q = εδ (Th4 - Tc4)A Where: q = Watts radiated ε : Emissivity (doesn't matter, set to 1 in this case) σ : Stefan-Boltzmann constant Th: Temperature of hot object in Kelvin Tc: Temperature of cold object in Kelvin A: Area of hot object exposed to cold object (can be assumed to be 1, or not particularly important in the application) That's great, so now I know the instantaneous power output. But I need to integrate this so I can have a formula that basically has time as an input and outputs the temperature of the hot object at some time after the initial conditions. It's been some time since my calculus classes sadly.