If you put "cold" honey frames in a "hot" extractor, the "cold" honey will flow out of the frames SLOWLY until the honey has had time to warm in the "hot" extractor. It will take time for the honey to warm inside the extractor. If you are only have a couple of supers to extract, and time doesn't matter, go for it. The honey will eventually warm and run out of the extractor. If you want the honey to come out of the frame faster, and run out of the extractor faster, then you need to heat the honey frames before you put them in the extractor. If you put warmed honey frames into a "cold" extractor, the honey will flow out of the frames quickly, and will also flow out of the "cold" extractor quickly, before it has time to cool and slow down.
If your honey is cold enough that it is not flowing out of your extractor after spinning out of the comb, then you need to warm the frames before extraction. This solves your problem. Heating the extractor instead of heating the honey frames can solve your problem, but it is less desirable because it will take longer to get what you want. I'd suggest not reinventing the wheel here. Generations of beekeepers before us, and with us now, have had to deal with the issue of extracting "cold" honey. The traditional and effective approach has been to warm the honey before extraction.
If you try going another direction and get better results, post it here and you could start a new trend.