A transient thermal analysis was conducted on the Tokamak Fusion Test Reactor vacuum vessel to determine the response of the vessel and its critical components to several pulsed discharge cleaning (PDC) and in situ bakeout scenarios. The three-dimensional model is described. The method of analysis, flow distribution, boundary conditions, and assumed configuration are stated. The resultant temperatures and thermal gradients are presented as a function of time and space on the vessel, bellows, bellows covers, ports, and port covers. Two PDC and three bakeout scenarios were analyzed. For nominal discharge cleaning, a 100-kW plasma with a 25-kW bellows ohmic heat (OH) dissipation was assumed. For aggressive discharge cleaning, a 400-kW plasma with a 100-kW bellows OH dissipation was assumed. In the first bakeout scenario a series of 56°C (100°F) temperature steps (ΔT) was imparted to the heating air at 10-h intervals until a bakeout temperature of 250°C was attained. In the second scenario the interval between steps was increased to 25 h. In the third scenario the temperature step (AT) was reduced to 28°C (50°F) at 10-h intervals between steps. The results of the analysis indicate that temperatures during initial operations can be maintained within allowable limits. A PDC maximum temperature of 232°C occurs on the bellows cover plates. The bakeout results show that for a 28°C step, 10-h interval, it takes 112 h to bake out the entire torus. Initial results of the thermal analysis enabled setting up in situ bakeout constraints that prevent excessive vessel/bellows stresses and minimized bakeout run times.