I dont know if it's just me BUT I have always been told by trainer's at gym's and such that when you are working out intensly on a machine and your heart rate is raised you are supposed to ease your heart rate back down, not just jump off the machine. I know if I do just jump off the machine my vision commonly get's blurry and I get a bit dizzy.
You'll notice on most machines they even have the cool down period programed in for you to follow.
But I've always noticed on the show that they will go from RUNNING INTENSLY to jumping right off a machine. If you think bakc to all the time's that Bob or Jillian have counted someone down, as soon as they get to one they remove their feet from the treadmil...is this healthy for your heart? I know it would really mess with my head!

I've noticed that too. I haven't been to a gym in a long time, but I sometimes would just get off the stationary bike or treadmill. Then I go and sit down. Maybe they do cool down, they just don't show it. I don't know.

I thought what we've seen is interval training.. High intensity for short spurts.. I think they do a mixture of things. Hard to tell how they mix it up as we only ever see snatchetts of the workouts..

It's obvious Bob and Jillian know what they are doing. They may also do stretching before and after.. or other light workout regimens..

Competitors who swim, run or bikers don't seem to need much transition.. They usually rest.. Runners I think try to walk a bit more for their legs than their hearts.. although it could be a combo..

Theories and practices seem to change constantly. I know when aerobics were popular that they had a warm up phase and a cool down phase.. Which I think just helps the muscles moreso than the heart..(which is a muscle too!).. Runners generally stretch their muscles before starting their runs/jogs..

As for TBL, we just don't see enough of the process to assume they don't do some warm ups and cool downs.. We just always see the more dramatic physical challenges. I trust Bob and Jillian.. I'm actually surprised that they don't have more physical injuries because of the intense workouts.. But we only see the intense aspects of the workouts and not the mundane stuff.

A lot of what it looks like they do interval training (which many studies have shown is far superior for burning fat, losing weight, and improving fitness than just doing long slow cardio workouts.) With interval training you work at max or near max capacity for short bursts and either take short rests or do a light interval to get your heart rate back down a bit before doing another high intensity interval (a good example would be sprint workout...sprint 100 yards, walk 100 yards, sprint 100 yards, etc.)

I'm sure they also do cool downs and stretching at the end of their workouts, but don't show it. Afterall, how many viewers really want to watch them cooling down? It's not as "dramatic" as showing them grimacing and dripping sweat everyplace.

Yes, stopping suddenly can cause a drop in blood pressure. Even with interval training or high intensity interval training, you should lower your heart rate a bit before stopping. Interval training is working out at different RPEs. You do short bursts of intense exercise followed by lower intensity exercise. It's different from steady state, which they also appear to do on the show.

That said, we see them stop, but we don't necessarily see the cool down on the show.