Abstract: The temperature field problem is solved by conformal mapping，the solution domain is transformed into a band domain or a semi-infinite band with an adiabatic boundary by the transformation function. Thus，the two-dimensional temperature function is reduced to a one-dimensional function，then the boundary value problem of the Laplace equation is solved expediently，and its temperature distribution function is given，and the isothermal map is drawn by software MATLAB.

Key words: conformal mapping, Laplace equation, reduced dimension method, temperature field, isothermal map