The paper presents an analytical solution for controlling the temperature distribution in infinite wedge domain. The objective is to assign the heat flux at the boundaries of the domain such that a desired temperature distribution inside the semi-infinite domain is achieved. Since the conduction equation (Laplace equation) retains its form when the infinite domain is transformed into a finite domain by conformal mapping, the infinite domain can be transformed into a disk of unit radius. Then the Laplace equation is investigated in the domain confined by a circle of unit radius. The control technique used in this paper is based on the Lyapunov approach. A Lyapunov functional is defined over the circular domain and the control heat fluxes at the boundary of the disk are assigned such that the time derivative of the Lyapunov functional becomes negative definite. Since the conformal mapping is invertible, attaining a desired temperature distribution in the circular domain leads to achieving the desired temperature distribution in the infinite domain.