No, not a regional thing. Hace calor is a general statement about the weather/temp. For ex. If it's35C. you would say hace calor. Tengo calor is about how you feel. It could be 10below, but if you are dressed too warmly you may feel too hot, and you would say tengo calor, even if hace frio.
As for caliente, it's the state of an object, how it feels to the touch. A hot plate = el plato esta caliente.
So it would go like this: hoy va hacer calor. Anuncian 35 grados. Espero no tener calor, pero ya se que la carretera se va poner caliente. Today will be hot.I hope not to be hot, but I know the tarmack will be hot. All three ways of saying it in Spanish! Voila!