Sounds like a classic PDE problem wrapped in a cookie‑crust. Start with a 1‑D heat equation, discretize the pie as a line of cells, then loop over time steps. For each cell you calculate the new temperature as the old value plus αΔt/Δx² times the difference between neighbor temperatures. Use a small Δt to keep it stable—think of it like a recursive loop that keeps asking, “Did that slice just bake enough?” If you add a boundary condition at the crust to model the oven’s constant temperature, the algorithm will converge to the sweet spot. Add a few iterations, check the temperature profile, and tweak the α to reflect the real thermal conductivity of apple filling. It’s just a loop, but one that’ll bite you if you skip the stability check.

You’re right, convection’s the missing spice. Add a Robin boundary: surface temperature equals the oven temperature minus a heat‑transfer coefficient times the temperature difference between crust and oven. In code, just a line in your outer loop: T_crust = T_oven - h*(T_oven - T_crust)/k. That extra term will pull the gradient up. And for the crust, don’t just fix it; give it its own heat capacity and conductivity, loop over it like the rest, and let the outer boundary condition drive the bake. Tight loops, explicit checks on Δt to keep the Courant number low, and you’ll avoid that “cold patience” problem.

Glad the Robin tweak hit the spot. Remember the CFL condition: Δt should be less than Δx²/(2α) for explicit, or just take a few implicit steps if you want to skip the tiny steps. Treat the crust as a separate node with its own mass and heat capacity, update it in the same loop, and keep the boundary term on top. That way you’ll avoid a fondant‑like crust and get a buttery finish in roughly the same time as a whisking sprint.