  In general, the Gibbons-Hawking temperature based on the Euclidean functional
approach shows that de Sitter space in the Bunch-Davies vacuum is globally
thermal. In the exactly soluble semiclassical Jackiw-Teitelboim model, we
investigate thermal property of de Sitter space by taking into account the
quantum back reaction of the geometry. The proper temperature of de Sitter
space in the Bunch-Davies vacuum is found to vanish. In case of a certain
quantum state breaking the de Sitter symmetry, de Sitter space can be made
thermally exited; however, in this case the dilaton singularity cannot be
avoided. Consequently, in the Jackiw-Teitelboim model the proper temperature of
de Sitter space in the Bunch-Davies vacuum turns out to be zero and the
Bunch-Davies vacuum is found to be the only physical vacuum without any naked
singularities.
