A CO2 laser beam, as an electro-magnetic ‘light wave’ at a frequency of 10,600 microns, contains a certain energy which is (partially) absorbed by the material. The photons, i.e. the ‘light particles’, transfer their energy to the atomic or molecular structure of the material, which in turn causes the material to heat up. If the energy of the laser is high enough and is allowed to work for long enough, the temperature required to vaporise the substance develops on the material.
Material 1 melts at approx. 140°C, material 2 at 230°C – with 200 W laser power, one can therefore cut material 1 faster than material 2, as the energy doesn't have to be applied for as long to material 1 as to material 2.
Consequently it can be said that a laser beam itself has no temperature.