Thermal stresses may be induced in a hot dry rock when a cold fluid is injected in the well. To study this problem, we look at the thermoelastic response of a hot rock that is suddenly cooled. The cooling is assumed to be either at a constant temperature or at a constant heat flux per unit depth. Our approach is to nondimensionalize the equations and perform a parametric study and look at the temperature distribution and the induced-thermal stresses. The results indicate that depending on the extent of cooling and the cooling time, thermal stresses can be induced. Numerical simulations on sandstone, with an initial uniform temperature of 473 K, are also carried out. The results show that if the cooling is due to the surface temperature maintained at 463 K (10 °C lower than the initial temperature of the hot rock), thermal stresses that are larger than the rock tensile strength could be induced. When the cooling is due to a constant surface heat flux, this temperature can be reached after about 777 days of cooling with a minimum value of a heat flux of −20 W/m.