Does heat have an effect on caffeine?

I suffer frequent headaches. One of the things that help, other than medication, is hot coffee. I know that caffeine is often used in headache medicine. I’ve taken caffeine in pill form and have had high caffeinated sodas. None of those seem to do much, but hot caffeinated coffee works for me. Has heat been known to amplify the effects of caffeine? If so, what’s the science behind that?