<p>In some laser-based applications, such as laser welding and surface hardening, it is significant to maintain the surface temperature at an elevated level for a certain period even after the laser is turned off. This study investigates the effect of a surface temperature-dependent absorption coefficient that may control the surface temperature in a specific period. The MGL theory is employed to analyse the effects of the surface temperature-dependent absorption coefficient in a nonlocal thermoelastic semi-infinite medium heated by a laser pulse. The volumetric absorption technique is used in the heating process for a medium whose surface is exposed to surface-dependent heat loss and is traction-free. The integral transformation method is used analytically to obtain a general solution for the problem and computationally to attain the inverse transformation. The results indicate that the absorption coefficient, which depends on the surface temperature, exhibits a temporal and spatial impact period. It significantly influences thermal waves, while its impact on elastic waves is minimal.</p>