To determine if an action is "worth it", we must evaluate its costs and benefits, and subtract the former from the latter.
What are the costs and benefits of heating food?
This clearly sums up everything there is to know about the matter. There are no other possible costs or benefits of heating food.
Assume the food is heated electrically. This may distort the true cost by perhaps half an order of magnitude in either direction. Other heat sources, such as natural gas, may be cheaper, but not necessarily by that much, and are less sustainable.
Assume the electrical energy converts to heat in the food with perfect efficiency. This may be optimistically wrong by perhaps up to an order of magnitude.
The price of electricity, in the US, is on the order of $0.20 per kWh. 1 kWh is 3.6 MJ, or 860 kcal, so that price is $0.00023 per kcal.
Assume the food savings take the form of avoided sugar purchases. Sugar has an unusually high calorie-price ratio. This may underestimate the true savings by maybe an order of magnitude. The assumption that calories from food-heating directly correspond to savings in unpurchased other food probably overestimates the true savings. I will assume these cancel out and move on.
The price of sugar, in the US, is on the order of $1.40 per kg. 1 kg of sugar has about 4000 kcal, so that price is $0.00035 per kcal.
A typical person eats around 2 kg of food per day. Assume your food has the specific heat capacity of water. Heating all of your food by 30 K entails adding 60 kcal of heat energy per day. That corresponds, by preceding calculations, to saving $0.021 at a cost of $0.014 per day.
Heating food appears to be worth it. However, the margin is tiny, and the estimate may have large errors in either direction. This also neglects other costs, benefits, and complications humans suggest as relevant, such as the pleasure of warm food and wasted heat from intermittent cooling.
The benefit described above takes the mechanism of a heated body, absorbing heat from food. Thus, you could get the same benefits by heating your body directly and eating less?
Probably, but not by heating your body arbitrarily; only by heating it towards its preferred temperature when the environment is colder.