Caliente is an adjective, then must be accompanied by a noun (before or after):
sopa caliente, agua caliente, "something" caliente.
Calor is a noun: Calor corporal (temperature), calor solar, calor humano, can be accompanied by a verb: Hace calor, tengo calor, el calor es extenuante.
Generally you use calor when referring to the weather or how you feel, e.g.
Tengo mucho calor. - I am very hot.
Hace mucho calor hoy. - It is very hot today (the weather).
Caliente is used more for things that can become hot and burn you, e.g.
Ten cuidado, el horno está caliente.