During intraluminal or intracavitary hyperthermia treatments, limited non-invasive temperature information is available, which may result in sub-optimal treatment control. This article describes a method for estimating temperature maximums and their corresponding locations in tissue heated by a cylindrical applicator with an incorporated cooling system, assuming a hollow cylinder of homogeneous tissue. The main purpose of this study is intraluminal heating of tumours at the oesophagus, but the principle described is generally applicable for cylindrical applicators. When assuming no perfusion and only radial heat flow in the heated tissue, an analytical expression for the temperature profile can be derived such that the complete profile can be reconstructed from the inner wall temperature only. For situations with perfusion, finite difference simulations have been performed and the resulting simulated inner wall temperature was put into the analytical expression to obtain an estimation for the maximum temperature and the corresponding location. This way, an estimation method was developed which does not require a priori knowledge of the perfusion rate or invasive thermometry. For volumetric perfusion rates in the clinically relevant range of 0-10 kg m-3 s-1, the deviations between simulated and estimated temperature maximums were less than 10% and the difference in location was typically a few tenths of a millimetre. These deviations are small enough for treatment control purposes.