The impact of climate change on human health has received increasing attention in recent years, with potential impacts due to vector-borne diseases only now beginning to be understood. As the most severe vector-borne disease, with one million deaths globally in 2006, malaria is thought most likely to be affected by changes in climate variables due to the sensitivity of its transmission dynamics to environmental conditions. While considerable research has been carried out using statistical models to better assess the relationship between changes in environmental variables and malaria incidence, less progress has been made on developing process-based climate-driven mathematical models with greater explanatory power. Here, we develop a simple model of malaria transmission linked to climate which permits useful insights into the sensitivity of disease transmission to changes in rainfall and temperature variables. Both the impact of changes in the mean values of these key external variables and importantly temporal variation in these values are explored. We show that the development and analysis of such dynamic climate-driven transmission models will be crucial to understanding the rate at which P. falciparum and P. vivax may either infect, expand into or go extinct in populations as local environmental conditions change. Malaria becomes endemic in a population when the basic reproduction number R0 is greater than unity and we identify an optimum climate-driven transmission window for the disease, thus providing a useful indicator for determing how transmission risk may change as climate changes. Overall, our results indicate that considerable work is required to better understand ways in which global malaria incidence and distribution may alter with climate change. In particular, we show that the roles of seasonality, stochasticity and variability in environmental variables, as well as ultimately anthropogenic effects, require further study. The work presented here offers a theoretical framework upon which this future research may be developed.