A new numerical algorithm for predicting three-dimensional temperature fields in tissue with large vessels is presented. The capabilities of the model were demonstrated by considering a thermally significant countercurrent vessel pair (600 μ in diameter each) embedded in an elemental tissue volume and feeding a tumor under hyperthermia. Tumor-peripheral heating with ultrasound was also considered. Results showed that under conditions representative of those that may be found in the clinic the arterial blood remained under therapeutic levels before entering the tumor volume. Peripheral heating was very effective in raising the temperature of the normal solid tissue surrounding the tumor and in pushing high temperature gradients away from the tumor margin; however, it was not sufficient to heat the arterial blood to therapeutic levels.