Abstract: In order to clarify whether heated object moving in homogeneous velocity receives leading-force and leading-work, the changes of total momentum of heated object at uniform velocity is analyzed from space-time attribute of physical quantity in special relativity, and the objective fact of producing time-like leading-force 4-vector only because of changing proper-mass is pointed out. The concepts of leading-force and leading-work in laboratory-reference-system are established and the process of inelastic collision between two bodies is examed. Using thermodynamic law, the leading-force, leading-work, and relativistic quantity of heat are calculated. We find that the relativistic quantity of heat is contractive than proper quantity of heat in infinitesimal process. 4-momentum-conservation equation is used in manybody system of ideal gas, and the contractive factor √1 - v₂/c₂ of the motion quantity of heat of closed global system is evaluated. It is exactly consistent with that of Planck-Einstein school. This result further validates P-E theory in relativistic thermodynamics.