Using the thermoporoelastic theory previously proposed, thermal stresses are analyzed that are induced in a fluid-saturated poroelastic hollow sphere, whose inner surface is exposed to burning gas and the wall of which is cooled by the fluid injection from its outer surface. Two loading histories are considered: (i) the sphere is subjected to a sudden rise in temperature of the gas and simultaneously pressurized at its outer surface to cool the wall; and (ii) steady-state cooling is abruptly disturbed by a sudden loss of pressurization and, after a while, is recovered. The main focus is on the effect of heat advection due to active fluid injection on the reduction of temperature and thermal stresses. Since the formulated problem is axisymmetric, the displacement field is decoupled from the temperature and pore pressure fields, which are still coupled to each other. The coupled nonlinear diffusion equations are solved by the Crank-Nicolson implicit method. It has been concluded that the active fluid pressurization and injection are effective in suppressing the maximum thermal hoop stress at the outer surface without the occurrence of the excess compressional stress at the inner surface.