In-cylinder heat transfer is important to the performance of many reciprocating energy conversion machines. It is particularly important to the performance of Stirling machines. For cylinder spaces without inflow, heat transfer and related power losses can be predicted using an analytical model which neglects turbulence. In actual engine cylinders, where significant turbulence levels can be generated by high velocity inflow, a model which neglects inflow may not be adequate. Several models have been proposed for in-cylinder heat transfer with inflow-produced turbulence. Existing models are based on the assumption that turbulence levels remain constant over the cycle. In the current work, experiments were performed to measure the effects of inflow produced turbulence on in-cylinder heat transfer. Experiments were conducted for two different inflow configurations. These experiments have shown that turbulence levels can change significantly over the course of the cycle, invalidating one of the major assumptions common to existing models. In response to the experimental results, a new model was proposed to predict the effects of variations in the turbulence level throughout the cycle. Based on the I-D energy equation, it extends an existing heat transfer model by replacing the laminar thermal conductivity with a time varying effective turbulent thermal conductivity. The varying component of the effective thermal conductivity is assumed to be small relative to the mean component, allowing the use of a perturbation method. Two Nusselt numbers were formulated based on the model results. The first was a complex valued Nusselt number. Previous work had demonstrated that a constant complex Nusselt number could effectively predict heat transfer throughout the cycle in cylinder spaces without inflow. For cylinders with inflow, the current model predicts a complex Nusselt number that varies over the cycle. The second Nusselt number was formed using the steady components of the second order temperature profiles. F or this steady Nusselt number, including the effects of thermal conductivity variations throughout the cycle resulted in a heat transfer coefficient that was larger than that predicted using a mean effective conductivity alone. / Master of Science