Thermal · photothermal heating
Yes, whenever the particle absorbs at the laser wavelength: metal particles in a trap can warm by many kelvin. The calculator gives the temperature from the particle's absorption in the focused beam.
The absorbed power and temperature rise of a sphere in a tightly focused laser of chosen numerical aperture and polarization, from generalized Lorenz–Mie theory.
No: the heating comes from the particle's own absorption. Near-infrared trapping lasers also heat water slightly on their own, which adds to it.
The temperature of a particle in a tightly focused trapping laser, in one click.