I don't even know what a tummy sweat belt is. I'm assuming it's a belt you wear around your midsection to make you sweat more?....Sorry, man, there's nothing that will make you burn more calories but more exercise or more intense exercise.
Sweat is just a cooling system for the body. Producing more or less of it have little to do with burning fat.
In fact, the better shape you are in, the less sweat you produce. Or from another point of view, the more fit you are the more it takes to produce the same amount of sweat that you used to produce when you were unfit.
Anecdotal evidence shows they work. This is because they have no biological function, but they do fulfill a behavioral need. To purchase one gives you the incentive to train harder and longer because you want to prove this (scientifically frivolous) investment right. If you lose weight, give yourself the credit.
Truth. Thermogenic effects of something like this are so mediocre they truly don't do anything at all. The only thing that will cause you to lose weight is being in a caloric deficit from your maintenance level of Kcal intake. Sorry man.