Abreu (1967) studied the two-dimensional ,inconpressible, constant vorticity flow past an infinite wedge. In the present work the problem solved by Abreu is considered for the case where a constant temperature fluid flows past an infinite wedge with non-isothernal surface, thus given rise to a thermal boundary layer. The matched asyntotic expansion netod,as present in Van Dyke(1962), was applied to the solution of the problem. According to Van Dyke there are four problems leads to the desired asynpotic solution for large values of the Reynolds number. The solution defines a system forned by the Navier Strokes, continuity and energy equations. The asym ptotic expansions found by Abreu (1967) for the hydrodynamic problem i.e for the continuity and Navier-Stokes equations were used in our solution. Although a general analytical solution was found for any angle of the wedge between 0 degree and 90 degrees numerical solutions are show for the particular semi-angle values of 0 degree, 18 degrees and 72 degrees and Prandt 1 numbers values of 0.7,1.0 and 10.