Goal: Micromagnetic stimulation using coils sufficiently small to be implanted has been suggested as a potential method to overcome the limitations of electrical stimulation. We investigated the temperature increases in the brain implanted with planar coils. Methods: We conducted computational simulations on the thermal effects of implantable magnetic stimulation in a brain model using finite-element analysis, by varying geometric parameters of planar spiral coils, and repetitive stimulation pulse patterns. Results: It was revealed that the temperature increase in the brain can be controlled by a careful design of coils to implant. The coil diameter greater than 8 mm was required to induce a temperature rise in the brain of less than 1 degrees C. If the coil diameter was larger than 10 mm, the subsequent temperature rises in the brain tissue was maintained consistently at about 0.24 degrees C or lower. Conclusion: Selection of the number of coil turns must rely on tradeoffs between the required current and voltage that the implanted source can generate, as the required voltage increases while the required current decreases with increasing number of coil turns. Additionally, the coil insulation with a thickness of a few micrometers was found to suppress the temperature rise in the brain effectively. Significance: Although these simulations employed only one threshold value of 10 V/m, which is rather on the lower end of stimulation threshold, the simulation results are expected to serve as guidelines for designing planar coils to be implanted in the brain for magnetic stimulation.