The theoretical analysis of thermal effects induced by nanosecond laser irradiation on bulk YBa2Cu3O7 superconductor targets provides insight into the nature of the target's ablation/evaporation characteristics during pulsed laser deposition of superconducting thin films. We have simulated the thermal history of YBa2Cu3O 7 targets under intense nanosecond laser irradiation by numerically solving the one dimensional heat flow equation and taking into account the phase changes occurring at the near surface of the target. The numerical method is based on a higher-order finite difference scheme with a smaller truncation error and is not restricted by any stability criterion, thereby allowing faster convergence to the exact solution. Temperature-dependent optical and thermal properties of the irradiated material as well as the temporal variation in the laser intensity can be taken into account by this method. During planar surface evaporation of the target material, the subsurface temperatures were calculated to be higher than the surface temperatures as a result of combination of two unique effects. While the evaporating surface of the target is constantly being cooled due to the latent heat of vaporization, subsurface superheating occurs due to the finite absorption depth of the laser beam. The effects of various laser and target parameters, including pulse energy density, pulse duration, absorption coefficient, thermal conductivity, and latent heat on the transient thermal characteristics of the irradiated target, have been investigated in detail. Subsurface superheating was found to increase with decreasing absorption coefficient and thermal conductivity of the target, and with increasing energy density. The superheating may lead to subsurface nucleation and growth of the gaseous phase which expands rapidly leading to microexplosions and "volume expulsion" of material from the target.