"...I thought the oven is left on for CPOP, and turned off if you simply want to ensure gel in regular CP? ..."
If you want to be a purist, cold process (CP) is soapmaking without added heat. So, no, putting the soap into a preheated warm oven doesn't qualify as CP. Putting the soap on a warm heating pad wouldn't be purist CP either.
And, again, if you want to be a purist, the CPOP method is cold process soapmaking with added heat from the oven. The general rule of thumb is about 170 deg F for about 1 hour.
But if I've learned one adage about soap making, it's this -- there are many ways to reach Rome.
If you can figure out how to modify the CPOP Rule of Thumb to gel your soap using less heat or less time, there are some real advantages. Some recipes, such as those high in coconut or scented with tricky fragrances, will overheat and crack, separate, or even volcano if you pop that baby into a 170 deg F oven and let it bake for an hour.
Less fussy recipes might also benefit from a shorter or cooler heating period: There will be less loss of fragrance from the soap. The texture on the top of the soap may stay a little nicer. There may be less soda ash on the top as well. Any botanical ingredients (including superfat) may be less prone to long-term deterioration and rancidity.
"...bake your soap for 4 hours at 60°C [140 deg F] (or for ~3 hours at 70-75°C [170 deg F] with air ventilation...)"
What a researcher does to meet the goals of a scientific experiment is one thing. What a soap maker might want to do to ensure good appearance and longevity might be another! Just a thought....