Personally, I wouldn’t add heat to my yoga practice if an injury is present. My hot yoga participation years were before I got my 200-hour yoga training, and I enjoyed the feeling of yoga in a warmer room. It definitely contributed to my ability to stretch a little farther.
That said, I was healthy with no injuries, and very regular in my yoga practice. i’d worry that someone with a pre-existing injury or a beginner would go too far into a pose without realizing it and exacerbate existing issues.
I’m not sure what you mean by “hot” yoga. Is that more of the astanga (sp?) type? Movement, especially loaded, certainly adds stress to the lower back. Stretching after the workout is best, the soft tissues are warmed-up. Typically I recommend supine single-knee, single-knee, double-knee. As far as progression, more sets and more reps.
While I would say that anyone with low back issues that is cleared for exercise can participate in most exercise class if they follow proper progression and form and that I feel yoga is a viable movement and balance system for this group if done with caution (and again proper progression, etc.), why do you need to add the element of a heated environment? What physiological response are you attempting to improve?
I don’t see how this is viewed as a good thing. Why not add high temperatures to all forms of exercise then? Did none of these instructors pay attention to the heat stress segment of First Aid? It is a fad, not a legitimate enhancement of yoga. Sure if you live in a place where it is always hot, you need to exercise and it may not be possible to have a cool place in which to do your exercise. But in this scenario you need to reduce intensity and duration accordingly. Then progress either parameter appropriately.
I would recommend the careful addition of standard yoga for such a client. If they enjoy it and are benefiting from yoga, why are you going to add the element of heat? If you want to do this, you need a very sound answer for “why?” you are doing it. Not just to do something new or popular.