This study aims to look into the temperature distribution on a vertical flat plate with a variable temperature boundary condition. As a novelty, the variable temperature is considered on the wall, and coupled momentum and energy equation are solved. Moreover, a novel variable change transforms the infinite boundary condition into the finite one. The partial differential governing equations were introduced and transformed into ordinary differential equations form using the similarity solution. The obtained equations were numerically solved and val-idated using previous research. The results showed that for a constant variable temperature index (n), increasing the Prandtl number (Pr) from 0.1 to 2 reduces the dimensionless max-imum velocity by less than half and the skin friction coefficient by about 32%. In this case, the dimensionless temperature approaches zero faster; as a result, the thermal boundary layer thickness declines, and the Nusselt number (Nu) rises. Furthermore, for a constant Pr, when n increases from 0 to 1.5, the dimensionless maximum velocity and the skin friction decrease by about 38% and 23%, respectively. Since the dimensionless temperature continues to descend-ing trend, Nu still rises in this case.