Of course not. This is a chemical kind of hot, usually due to capsaicin in the food, nothing to do with actual heat. Capsaicin stimulates your taste buds to THINK you're tasting something hot, but it's all a chemical reaction.
Which is why drinking something cold doesn't always help with the burning sensation. What works best to calm it down is to eat something with fat in it - that blocks the chemical. A popular side dish in India to go with hot curries is raita, which is a mixture of chopped cucumber and yogurt. They know what they're doing! On the same principle, if you want a cold drink to calm down that burning sensation, the best thing is a glass of full-fat milk. I tell you, it works, and it's been scientifically proven to work in tests.