A finite time thermodynamics analysis is performed for a solar driven heat engine. The collective role of the radiation and convection modes of heat transfer are investigated. Heat transfer from the hot reservoir is assumed to be radiation dominated, while convection heat transfer is assumed to be the main mode of heat transfer to the low temperature reservoir. The irreversibilities due to these finite rates of heat transfer were considered in determining the limits of efficiency and power generation that were discussed through varying process parameters. It is shown that the Curzon-Ahlborn efficiency is not a fundamental upper limit on the efficiency of cyclic heat engines operating at maximum power conditions. This upper limit is a function of both the functional temperature dependence and of heat transfer and relevant system parameters.