This paper presents a selection of data from an investigation that was concerned with the heat transfer which occurs when an under-expanded jet impinges onto a heated cylindrical surface. The purpose of the study was to establish the thermal boundary conditions for calculating thermal stresses in heat transfer surfaces when subjected to high-speed cleaning jets. The heat transfer in the impingement zone of a high-speed jet is extremely high and when the presence of the surface interferes with the expansion of the jet, the radial and circumferential distributions of the heat transfer coefficient become complicated. If a highly under-expanded jet impinges upon the surface while the nozzle-to-surface spacing is small, z=D % 3, there is no longer a maximum stagnation heat transfer coefficient on the geometric axis of the jet, instead a stagnation ΓringΓ is formed with a radius of about one nozzle diameter. A selection of data is presented that shows how, particularly for z=D less than 10, the Nusselt number distribution has a very high peak value at, or near to, the geometric stagnation point and then falls away steeply in both the axial and circumferential directions. The high values of Nusselt number, and the large differences between the peak values on the front edge of the cylinder and the values at the rear of the cylinder, could lead to very substantial differential cooling rates and hence to significant thermal stresses being generated when high pressure air cleaning jets are used on high-temperature tubes. However, when the nozzle exit is placed more than 20 nozzle diameters away from the surface of the cylinder there is a significant reduction in the maximum Nusselt number and the overall distribution is much smoother; this will alleviate potential problems from thermal stresses.