The practical use of a discrete vessel thermal model for hyperthermia treatment planning requires a number of choices with respect to the unknown part of the patient's vasculature. This work presents a study of the thermal effects of blood flow in a simple tissue geometry with a detailed artificial vessel network. The simulations presented here demonstrate that an incomplete discrete description of the detailed network results in a better prediction of the temperature distribution than is obtained using the conventional bio-heatsink equation. Therefore, efforts to obtain information on the positions of the large vessels in an individual hyperthermia patient will be rewarded with a more accurate prediction of the temperature distribution.