A method has been developed to heat and control temperature in a two-dimensional monolayer dusty plasma. A monolayer of highly charged polymer microspheres was suspended in a plasma sheath. The microspheres interacted with a Yukawa potential and formed a triangular lattice. Laser manipulation was used to apply random kicks to the particles. Two focused laser beams were moved rapidly around drawing Lissajous figures in the monolayer. The kinetic temperature of the particles increased with the laser power applied, and above a threshold a melting transition was observed. Characteristics of a thermal equilibrium of the laser-heated dusty plasma in solid and liquid states are discussed.