It sounds like the PDE outputs a latent variable – temperature – which somehow determines the probability of whether a fire is observed (either True or False) at a given coordinate. So the actual data generating process could be modeled as a 2d matrix of Bernoulli random variables – fire or no fire – with the probability parameter p \propto f(temp). f would be some linear function wrapped in a sigmoid, like \sigma^{-1}(\alpha + \beta * \text{temp}) so the probability is between 0-1. This would match your data, as now the model will just output a 2d mask of 1’s and 0’s, since that’s what a Bernoulli does.
I think this might be similar to another question that was asked about golf. Maybe it could be helpful?