This thesis investigates heat transfer processes occurring in microcombustors. First, a simple 2D model is developed for predicting temperature profiles in a premixed laminar flame propagating between two parallel plates. The model is used to generate a correlation for the variation in Nusselt number with downstream distance which is useful for numerical simulations. It also shows that the temperature profile across the channel is well approximated using either 2nd or 4th order polynomials. Second, the functional form of the gas temperature profile is used to demonstrate a new diagnostic technique for making non-intrusive measurements of gas temperature and wall heat fluxes. The technique is applied in a silicon-walled microcombustor (5 cm x 2 mm x 5.5 cm). The gas temperature and wall heat flux measurements are combined with measurements of the wall temperature distribution to develop a complete picture of heat transfer in the microcombustor. The results show that thermal feedback from the post-flame to the pre-flame via the structure is the dominant heat transfer path in microcombustors.