A globally averaged energy balance climate model with a deep ocean reduced to the one-dimensional case is used to study the transient thermal response characteristics of the system. Analytical solutions are presented for the upwelling diffusion and the box diffusion models for a general radiation forcing function in terms of a convolution integral. An exact solution for a step change in upwelling rate is presented, and an approximate solution for small variations in upwelling rate about some initial value is presented. Comparison between the exact and the approximate solutions indicates that the approximate transient response due to a time-dependent upwelling fluctuation is accurate for ‖Δw/w0‖<0.02. The transient thermal response of surface temperature due to radiation forcing of an upwelling diffusion model is found to be significantly more rapid than that of the box diffusion model.