Don't think it will work because the heat drawing the oils from the plastic is what makes it dry and chalky in the first place so applying more heat would only make it worse and speed up the natural ageing process. I have seen plastic motorcycle tanks and fenders restored by removing the chalky layer and fine sanding and then polishing the fresh surface but this process would be useless for trim as you would remove the texture or grain and end up with a smooth not correct surface.