In local hyperthermia, the goal is to raise target tumor temperatures to a uniform therapeutic temperature (i.e. 41–45 °C) with minimal injury to normal tissues. However, existing thermally significant blood vessels within or near a tumor makes hyperthermia treatment difficult as the traditional 1st-order iterative adaptive power scheme is unable to heat the tumor fast enough during treatment . Strong convective heat transfer by large blood vessels is the main reason. The objective of this paper is to investigate a novel fast adaptive power scheme when a pair of counter-current blood vessels (artery-vein) is present in a tumor being treated with hyperthermia. Convergence value (CV) represents normalized root-mean-square deviation (NRMSD) of temperatures (with respect to therapeutic temperature); this value is used in the study to search for optimal power deposition. Higher order power deposition schemes (up to the 7th order), two counter-current blood vessels, and various distances between large artery and vein have been proposed and tested in computer simulations. The results show that the new scheme is robust with more than one large blood vessel under considerations. The scheme is capable of estimating power density deposition with accuracy in a short time, and interestingly reveals “scheme mismatch” which could speed up the convergence process.