A basic study on the convective flame-wall heat transfer in diesel engines was performed with a fundamental experiment and simplified theoretical models. Based on the concept of flame tubes, a combustor was designed and optimized to support laminar, stable flame propagation at constant ambient pressure. Measurements of flame position and heat transfer during head-on quenching of premixed methane-air flames with varying mixture equivalence ratios at a metallic surface were made using flame luminosity videography and surface thermometry. Two models were developed to predict the magnitude of single-wall quenching layers and the flame-wall heat transfer at a variable temperature wall. One of the models was a quasi steady-state first law balance which utilizes an Arrhenius reaction equation to represent the temperature sensitivity of the chemical processes according to a single-step reaction mechanism. The second model was based on transient heat conduction theory; a planar, moving heat generating sheet simulated the heat release of a propagating flame front in a one-dimensional slab of gases at rest, bounded at the wall at which quenching occurs. Experimental and model results showed that flame-wall heat transfer is primarily dictated by the reaction rate of combustion and the thermal diffusivity of the gas mixture. The convective heat transfer coefficient was predicted to increase with rising wall temperature. Measured peak heat transfer rates were 25% higher than those reported in the literature. Recommendations are made for the design of an experimental apparatus with which conditions encountered in internal combustion engines can be simulated more closely.