The isothermal surface equation of tri-band radiation thermometry with linear emissivity model has been deduced, based on tri-band radiation measurement equations. The isothermal surface equation is the point multiplication of measurement signal vector and measurement signal coefficient vector. The solution algorithm for tri-band radiation thermometry defined as dichotomy with coefficients stored in this paper has been developed because of the characteristics of measurement signal vector which is only the function of temperature and the advantage of dichotomy in solving non-linear equation. And the solution algorithm has been achieved by C++ program. The curves of isothermal surface equations at specific measurement signal vectors have been investigated and the results show that the curves are monotone at a greater range of temperature and the tail of curves tend to be positive from minus with the increase of V3. The analyses of error and time complexity have been carried out and the results show that the maximum error is (Tmax-Tmin)/2num+1 when the number for the solution algorithm is Num, and there are about 3Num+1 multiplication and 2Num+1 addition in every dichotomy process without division and logarithm, which can crease the solving rate dramatically.