As I understand it, this is a mantra meditation, 15-20 minutes, twice per day. If I remember, there is also a lot of money to be paid for it. And finally, there are claims of advanced program that will give you siddhis. (supernatural powers) Your red skeptical flag is waving rightfully. Try what you want, but don't pay money for it, not for Transcendental Meditation.

I have best experiences with Transmission Meditation, which is a bit more demanding, let's say 2 hours on average at least once per week, and has to be done in group at least of three. But at least it won't cost you anything. The only problem for some people is, that it requires you to pronounce the G-word a few times in initial invocation.
What good did this meditation for me? People say I became more normalized, less awkward, dreamy and escapist, after year or two of doing Transmission. Not that this process would be finished to my satisfaction, but it's still a great progress.

Anyway, I would recommend extensive meditation to people with both feet firmly on ground, with all paddles in water and with no bats in belfry, if you know what I mean. With mentally unstable people meditation might upset their wobbly status quo and send them flying in unwanted direction. It's really good to be firmly mentally grounded, that makes you safer even if you smoke pot.

Simple meditation of pretty much any kind is like mental cardio- it's doing a whole lot of something easy, and not getting much out of it beyond potentially a little stress relief (e.g. you aren't really building mental muscles, in the sense a proper work-out would do, just burning calories).  You could just as easily jog or do jumping jacks instead- that can also de-stress, depending on the source of it.

I guess 'pointless' meditation is like a lazy person's way to de-stress, without having to worry about the pesky side-effect of physical fitness...

If you want to de-stress, my advice is to get into jogging.

If you actually want to improve mental acuity, you can't just do something lazy like meditate- you have to do something substantially complicated- like learning mathematics, or solving difficult mental puzzles.  I.e. actual strength training.  To be fair, there are more intensive forms of meditation, but they aren't any easier than mathematics or mental puzzles, nor are they likely any more effective.

It's the same reason you don't jog to build strength.

Meditation is only really useful for a small number of practical things, which are easily supplanted by arguably *more*practical things, and that's only if you have a substantial amount of will power.

1. Sleep:

I can do a short meditation to fall asleep (and it's a quick way to hallucinate on the cheap if you're into that/think it has any value on its own [something I tend to disagree with]), but I don't really like to unless I can't get to sleep normally.  I prefer to just be flat out exhausted when I go to bed.

Non-meditation replacement:  Work out and make yourself tired.  Sleeping pills.

2. Cold:

I can get the equivalent of a placebo effect out of it- augmenting temperature experience or blocking out pain, etc.  I used to do this in sub-zero weather in a t-shirt, but that's actually a bad idea because it can't stop frost bite!  All if can do is change perception.  I'll only do it if the temperature is above zero these days.

Non-meditation replacement:  A coat.  Or, again, exercise.

3. Heat?

This is more hypothetical.  Usually when I'm hot, I'm irritated that I'm sweating and making my clothes smell... I probably can't stop myself from sweating, so I've not really bothered with this much.  Eliminating the perception of being hot, though, probably wouldn't be difficult.

Basically, stuff like that.  All things you'd get from a convincing placebo.  It requires a small amount of constant concentration, though, sort of like counting two piles of things at once (or like keeping score in a game without a score board).  Lose count, and you screw up and have to start over again.  It's rarely practical as more than a parlor trick.  And if you just woke up so you're a little disoriented and shivering like mad, it's very hard to focus enough to start counting coherently.

When one is awake enough to focus, though, it is fun to go outside in a t-shirt and shorts in a snow storm and laugh at the puny mortals... *

*provided the temperature outside is a hair above the actual freezing point of the slightly saline liquids in the body to prevent cell damage in extremities.