We explore an approach to incorporating task and motor thermal dynamics in the selection of actuators for legged robots, using both analytical and simulation methods. We develop a motor model with a thermal component and apply it to a vertical climbing task; in the process, we optimally choose gear ratio and therefore eliminate it as a design parameter. This approach permits an analytical proof that continuous operation yields superior thermal performance to intermittent operation. We compare the results of motor sizing using our proposed method with more conventional techniques such as using the continuously permissible current specification. Our simulations are run across a database of commercially available motors, and we envision that our results might be of immediate use to robot designers for motor as well as gearbox selection.