The laser beam of an Ar+-laser used for the laser recrystallization of silicon-on-insulator material in a three-dimensional integration process can contain large contributions from higher transversal electro-magnetic (TEM) laser modes of which the doughnut shaped TEM01*-mode is by far the most important one. An analytical expression is derived for the surface temperature of a bulk silicon wafer irradiated by a pseudo-stationary mixed-mode TEM00-TEM01* laser spot. The melt threshold of the irradiated wafer is determined as a function of the TEM01*-mode contribution and as a function of the ratio of the laser power absorptance in the liquid to the laser power absorptance in the solid material. The influence of the TEM01*-mode contribution on the size of the mixed solid-liquid `slush'-zone is studied quantitatively.