Temperature and thermal stress distributions in a two-dimensional infinite thin plate subjected to a moving heat source with variable power and velocity are obtained by solving quasi-static thermoelasticity equations analytically with the aid of a thermoelastic displacement potential. The results show good agreement with experimental data for a stationary source with constant power and with a steady-state analytical solution in the open literature. It is shown that the quasi-static solution can predict changes of the thermal stress field during the movement of the heat source, and can give the effect of changes of power and velocity of the heat source on the thermal stress field during its movement.