Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China
It is found that there is no period in the imaginary Beltrami time of the de Sitter spacetime with Beltrami metric and that the "surface-gravity" in view of inertial observers in de Sitter spacetime is zero! They show that the horizon might be at zero temperature in de Sitter spacetime and that the thermal property of the horizon in the de Sitter spacetime with a static metric should be analogous to that of the Rindler horizon in Minkowski spacetime.