  The temperature associated with gravitation as presented in the Unruh effect
and Hawking temperature serves to link different areas of physics, such as
gravity, statistical mechanics, and quantum physics. In this paper,
teleparallel gravity is considered to study temperature effects on the de
Sitter space-time. The effects of temperature are introduced using the Thermo
Field Dynamics (TFD) formalism. The gravitational Stefan-Boltzmann law is
obtained. Then the temperature of gravitation in the de Sitter space-time is
calculated. Here an Unruh-type effect is discussed. This effect relates the
temperature and the acceleration of a particle in the de Sitter space-time. The
gravitational Casimir effect is calculated. The result shows that there is a
transition between an attractive and a repulsive Casimir effect.
