Getting enough sleep is not just important to maintain sanity but also to help your body produce enough of fat-burning hormones like testosterone and HGH. Lack of sleep can disturb the circadian rhythm of your body and lower the secretion of these vital hormones and this can even speed up the aging process.
There's no denying the fact that fat burners which have stimulants like caffeine in them can play havoc when it comes to sleep. So, the best way to use them is to have them in the morning or afternoon. In any case, you should have it by 3 pm in the late noon and avoid having it after that.
However, if you suffer from sleep apnea then its best to avoid a fat burner that has stimulants in them. You can certainly opt for stimulant-free formulas.