The aim of this paper is to model the level of volcanic activity on Earth-like planets over time. We consider the level of volcanic activity on a planet to be a function of the planet’s thermodynamic state. A planet is considered to become volcanically inactive once it has reached a thermodynamic steady state. We first model the heat flow in the planet’s interior by the heat equation, which we reduce to a one-dimensional Laplace equation. We then calculate the temperature field of the planet by numerically solving a spherically symmetric boundary value problem. Finally, we relate discrete time-steps in our simulation to real-time via an empirically-informed mapping. Our results indicate that Earth will remain volcanically active for a total of ∼6.0\sim 6.0 billion years since its formation, while Earth-like planets of 0.50.5 and 2.02.0 Earth masses will be active for ∼5.5\sim 5.5 and ∼7.7\sim 7.7 billion years respectively. Our model incorrectly predicts that Earth-like planets above 2.02.0 Earth masses continually increase their internal temperatures if their conductivity and density profiles are assumed to be identical to that of Earth, which suggests some limitations of the model.