A three-dimensional conduction model has been developed to predict the transient temperature distribution inside a thick solid that is irradiated by a moving laser source, and the changing shape of a groove carved into it by evaporation of material. The laser may operate in CW or in pulsed mode with arbitrary temporal as well as spatial intensity distribution. The governing equations are solved using a finite difference method on an algebraically-generated boundary-fitted coordinate system. The accuracy of the present transient model was verified by comparison with previous three-dimensional codes that were limited to quasi-steady CW operation. Groove shapes and temperature distributions, as well as their transient development, for various machining conditions are presented, demonstrating the differences in the ablation process between CW, pulsed and Q-switched (or other pulses of extremely short duration) laser operation.