Do you burn more calories in the heat?

You burn about the same amount of calories whether you are running in a hot or cold environment as long as your running ability is not affected by weather-related conditions. You burn more or fewer calories due to the weather if it affects how much oxygen you need.

Running economy is the amount of oxygen you need to maintain a certain pace. If your running economy suffers because you are struggling to carry the weight of extra layers in cold weather, then you need more oxygen to maintain pace, and therefore expend more calories. If your running form suffers in the heat, you may actually expend fewer calories because you cover fewer miles.