I started searching, assuming there would be no evidence. I was happy to find there was actually some - perhaps not the strongest, and not enough to start recommending that you take the tablets, but at least there was some.
The two most relevant studies I found were these two:
For two days, they watched what 12 men and 12 women chose to eat from a small selection in a lab restaurant, after the subjects had either swallowed 0.9g of Red Pepper*, capsaicin pills or a placebo, with tomato juice.
CONCLUSION: In the short term, both oral and gastrointestinal exposure to capsaicin increased satiety and reduced energy and fat intake; the stronger reduction with oral exposure suggests a sensory effect of capsaicin.
* Cultural note: They are Dutch researchers in an international journal: I think they are referring to small chilli peppers, not large bell peppers (a.k.a. capsicum).
- H.C. Reinbacha, A. Smeetsb, T. Martinussenc, P. Møllera, M.S. Westerterp-Plantengab, Effects of capsaicin, green tea and CH-19 sweet pepper on appetite and energy intake in humans in negative and positive energy balance Clinical Nutrition
Volume 28, Issue 3, June 2009, Pages 260–265, doi: 10.1016/j.clnu.2009.01.010
In this study, they looked at 27 people over three weeks, where they were given various treatments of: capsaicin, green tea, CH-19 sweet pepper, capsaicin + green tea or placebo. They were also given either enough calories or insufficient calories to meet their "energy balance".
CH-19 sweet pepper and a combination of capsaicin and green tea reduced energy intake during positive energy balance. Capsaicin and green tea suppressed hunger and increased satiety more during negative than during positive energy balance.
Note: This paper has two co-authors in common with the above one, so should NOT be seen as independent confirmation.
In a third report from some of the same co-authors, they claim:
Capsaicin has been shown to be effective, yet when it is used clinically it requires a strong compliance to a certain dosage, that has not been shown to be feasible yet.
On top of these small, brief human studies, there have also been a number of animal studies, which I won't go into, but list a couple of examples:
There is some promising evidence, but what I saw was based on very small trials, didn't look at the long-term risks, didn't demonstrate that the effects are sustained, and wasn't independently replicated.
That's not enough evidence to suggest spending money and risking side-effects by taking these tablets - especially as doses are hard to maintain - but it is enough to pique the scientific interest