I want to roast an eggplant over a fire, and rotate it so that it receives an even heating over time. How do I do this?

For mathematical details, see https://math.stackexchange.com/questions/4387472/rotating-a-3d-shape-so-that-it-gets-heated-evenly-by-a-fire

As a computer science specialist, all I can think of is the following algorithm: take a running integral of the heat each point of the surface is getting, and greedily rotate towards whatever point has the lowest cumulative heat. This is a completely numerical algorithm, however, and I'd love if one of you mathemagicians could give something smarter.