The aqueous thermal boundary layer near to the ocean surface, or skin layer, has thickness O(1 mm) and plays an important role in controlling the exchange of heat between the atmosphere and the ocean. Theoretical arguments and experimental measurements are used to investigate the dynamics of the skin layer under the influence of an upwelling flow, which is imposed in addition to free convection below a cooled water surface. Previous theories of straining flow in the skin layer are considered and a simple extension of a surface straining model is posed to describe the combination of turbulence and an upwelling flow. An additional theory is also proposed, conceptually based on the buoyancy-driven instability of a laminar straining flow cooled from above. In all three theories considered two distinct regimes are observed for different values of the Péclet number, which characterizes the ratio of advection to diffusion within the skin layer. For large Péclet numbers, the upwelling flow dominates and increases the free surface temperature, or skin temperature, to follow the scaling expected for a laminar straining flow. For small Péclet numbers, it is shown that any flow that is steady or varies over long time scales produces only a small change in skin temperature by direct straining of the skin layer. Experimental measurements demonstrate that a strong upwelling flow increases the skin temperature and suggest that the mean change in skin temperature with Péclet number is consistent with the theoretical trends for large Péclet number flow. However, all of the models considered consistently underpredict the measured skin temperature, both with and without an upwelling flow, possibly a result of surfactant effects not included in the models.