The teleparallel gravity, in the weak field approximation, is considered. In the Schwarzschild space–time the gravitational Stefan–Boltzmann law is calculated. Using the first law of thermodynamics, the Hawking entropy and temperature of the black hole are calculated. Thermofield dynamics formalism is used to define the temperature-dependent theory. In addition the gravitational Casimir effect and Stefan–Boltzmann law at zero and finite temperature are calculated in Schwarzschild space–time.