Abstract: In this work, the problem of the propagation of a deflection wave in a Bernoulli–Euler beam during motion of the thermal source is solved, and the influence of the thermal bending moment and longitudinal force is analyzed. It has been established that the concentrated bending moment moving together with the heated region boundary determines the mode of the deflection wave, but cannot lead to a significant increase in its amplitude. It is shown that the average longitudinal compressive force increases linearly with time during uniform motion of the heating source. For the initial parameters, such as the source motion velocity and the temperature, the values enabling a loss of stability and a significant increase in deflection have been found.