The verification of thermal models for use in hyperthermia treatment planning is essential. We investigated the heat transfer between a single vessel and the surrounding vascularised tissue, comparing the conventional bioheat transfer theory and the recently developed keff model using analytical and numerical methods. A plastic tube inserted into the tissue of an isolated perfused organ served as an artificial vessel. This enabled us to vary the blood flow in the vessel and in the tissue independently. The organ used was a bovine kidney, turned into a perfused tissue phantom using an alcohol fixation technique. The temperature profile within the tissue was mapped with constantan-manganin thermocouple wire sensors with a total diameter of 50 microns. The temperature profile relative to the temperature difference between the vessel and organ was measured; increased perfusion caused a reduction of the vessel wall temperature but did not affect the width of the profile. Studying the transient tissue temperature after a step-wise change of the blood temperature in the vessel revealed a faster diffusion of heat at higher perfusion rates. These facts are in accordance with the keff model, but not with the conventional heat-sink theory.