I actually bought the entire kit from finafarm, the one with the DVD and everything, and I watched the video. (Although I had previously made a 2g kit from pumpnpose.)
Finafarm strongly recommends that the solution not be heated and I tend to agree. The probability of damaging the solution with heat or damaging the vial in some way would seem much greater than that of getting an infection from a properly prepared solution. The Whatman filter itself is capable of rendering the solution sterile from my understanding, much less the alcohol.
I've heard of various ways the heat can damage the solution, I'm not a chemist so I don't care to argue it to any great degree. But I would theorize one way might be that particles could be created larger than the Whatman had filtered out. I know that I unwisely tried to microwave at one point during the process with my first kit (after prefiltering but before filtering through the Whatman) and the Whatman clogged up fairly quickly. Of course that could have been for a variety of reasons, but again, in my estimation even the chance of damaging the stopper or something of that nature is more likely than getting an infection from the properly prepared solution. Too, I worry that baking causes evaporation of the alcohol, but again I'm not a chemist.