The 'go to' partial differential equation here is surely the Heat equation (Fourier), here in one dimension:
$$\frac{\partial T}{\partial t}=\kappa \frac{\partial^2T}{\partial x^2}+\frac{\dot{Q}(x,t)}{c_p\rho }$$
It can be easily expanded into three dimensions or expressed in polar, spherical or cylindrical coordinates.
It's not clear from your question whether these 'pulses' are really just short (or intermittent) bursts or continuous forms of irradiation. That would have to determined to define the source term $\frac{\dot{Q}(x,t)}{c_p\rho }$.
If you have some idea of the temperature in the 'spot' after a 'pulse', then you can drop the source term and use that temperature as an initial condition. The equation should then be easily separable:
Say for two dimensions, $T(x,y,t)=X(x)Y(y)\Theta(t)$. Insert into the 2D PDE to obtain three ODEs for $X$, $Y$ and $\Theta$.
Including a sketch of the geometry of your problem in your question would help decide the 'optimum' coordinate system to use. I'm quite interested in helping out with this problem but it does lack some information to take this any further.