In local hyperthermia, to raise target tumor temperatures to a uniform therapeutic temperature (i.e. 43~45 ℃) with minimal injury to normal tissues is the key treating process. However, existing thermally significant blood vessels within or near a small tumor area makes hyperthermia treatment very difficult as traditional 1st-order iterative adaptive power scheme is unable to heat the area fast during treatment. Strong convection heat transfer by vessels is the main reason. The objective of this paper is to investigate a pair of counter-current blood vessels (artery-vein) in a treated tumor area under a new proposed fast adaptive power scheme with features of controlling parameters, sentinel convergence value (SCV) and high temperature residual terms, in an attempt to reach uniform therapeutic temperature in tumor. Convergence value (CV) represents normalized root-mean-square deviation (NRMSD) of temperatures and is used in the study to search fast optimal power density deposition in hyperthermia treatment. Higher order power deposition schemes (up to the 7th order), two counter-current blood vessels, and various distances between artery and vein have been proposed and tested in computer simulations. The results show the new scheme is robust and capable of estimating power density deposition with accuracy in a short time and reveal “scheme mismatch” which could speed up the convergence process.