The depletion of volatiles from the earth's mantle over its history may have had significant effects on thermal convection, due to the effects of volatiles on silicate rheology. Experimental data suggest that the activation energy for solid‐state creep in a volatile‐free environment is as much as 25% greater than in a volatile‐rich environment, and thus devolatilization can lead to a substantial increase in viscosity. In a devolatilizing system, gradually increasing temperatures (relative to those in a system with volatile‐independent rheology) may be required to maintain moderate viscosities and convection. We investigate this postulated effect by incorporating a time‐dependent increase in activation temperature, simulating progressive mantle devolatilization, in a parameterized convection model. Volatiles significantly affect the earth's thermal evolution when the dependence of mantle rheology upon volatile content is sufficiently strong, the total volatile loss is sufficiently large, and devolatilization is relatively slow and continuous. For models with an increase of 20% in activation energy over earth history, the present‐day ratio of heat production to heat loss (Urey ratio) approaches or exceeds 1.0 when volatile loss is relatively continuous. With rapid early volatile loss, the upper bound on the present‐day Urey ratio is about 0.8 to 0.9, comparable to the limit with volatile‐independent rheology. Present uncertainties in these factors permit an earth that may be close to a steady thermal state or perhaps even warming up.