If you're cooling your house with electricity, or can't cool your house, and have the option to cook outside, the calculation that matters is how much electricity will it take to get your home back down to temperature again.
Either way, you're burning energy to eat. But in one scenario, you need to expend more energy to get that unwanted heat out of your once-cool living space.
I agree that perhaps the grill is much less efficient. I wouldn't cook directly on it, and if it had room to add more lava rock, I would do that. In addition, I think that I would use cast-iron pans on the grill, or better yet, an enamelled dutch oven. That would
boost heat retention greatly, but you'd still want to plan to do one-pot meals and store leftovers.
The two suggestions I might make, if you have electricity, is to think about a slow cooker. The other would be an induction hotplate. Either would be more efficient than a propane grill in the heat, especially if your electricity is
solar or wind-derived.
If it's expensive of difficult to cool your house down again, try to find ways to avoid it.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein