Thermal contact conductance is highly important in a wide variety of applications, from the cooling of electronic chips to the thermal management of spacecraft. The demand for increased efficiency means that components need to withstand higher temperatures and heat transfer rates. Many situations call for contact heat transfer through nominally cylindrical interfaces, yet relatively few studies of contact conductance through cylindrical interfaces have been undertaken. This study presents a review of the experimental and theoretical investigations of the heat transfer characteristics of composite cylinders, presenting data available in open literature in comparison with relevant correlations. The present investigation presents a study of the thermal contact conductance of cylindrical interfaces. The experimental investigation of sixteen different material combinations offers an opportunity to develop predictive correlations of the contact conductance, in conjunction with an analysis of the interface pressure as a function of the thermal state of the individual cylindrical shells. Experimental results of the present study are compared with previously published conductance data and conductance models.