An analytic solution for the temperature of the mixed layer for a box diffusion model of a global ocean is derived. It is shown that the analytic solution for the temperature of the mixed layer is expressed in terms of error functions. Arguments of the error functions are, in general, complex. It is shown that the exact solution approaches the appropriate limits of a mixed layer ocean model and of a diffusive ocean without a mixed layer on top. The effect of random noise on the temperature response is considered. Scaling transformations are used to derive the analytic solution for the box diffusion model which, in the case of the doubled CO2 experiment, depends on only one parameter. This dependence on one parameter permits derivation of a simple expression for the e-folding time and formulation of a quantitative sensitivity analysis for the response of the temperature of the mixed layer to changes of the parameters of the global ocean-atmosphere model. The sensitivity analysis is extended to include forcing functions which are integer powers of time. ¿ American Geophysical Union 1988