You can find a good description of cw or pulsed laser irradiation in the book "Laser Processing and Chemistry" of Dieter Bäuerle (available in its 4th edition):
To measure, you can consider the convective flow. With input such as spot size, beam effective area, the energy can be estimated. For guidance, some links are as follows.
Apart from the laser spot, you need to consider the substrate property also. I have done some calculations on the measurement here Article Gold Nanostars in Plasmonic Photothermal Therapy: The Role o...
The light in the laser beam shouldn't be thought of as heat. It doesn't have a thermal distribution of energies. In fact, with all the photons having very nearly the same energy and all traveling together in very nearly the same direction with nearly the same phase, and often with the same polarization, it is one of the least thermal things you can think of. However, that shouldn't confuse anything. The power in the beam is what they say, 1 mW or whatever. It just can't be called heat.
When the laser strikes a surface the surface may absorb some of the laser energy and/or reflect some of it. In most cases almost all of the part which is absorbed goes into heating the absorbing material. The thermal energy deposited in the surface is equal to the power of the laser beam times the fraction that is absorbed times the time the laser is on.
If you would like to know the density of the deposited energy (and from there the temperature the material reaches) you would need to know the intensity profile of the laser spot on the surface. However, you would also have to think about how the deposited energy is thermalized and transported away from spot where it is absorbed.