I have trouble sleeping at night and usually get 5-6 hours max. I lift 3x's a week and do cardio 2-3 times a week (including heavy bag work). Does afternoon napping help with recovery? How does it affect fat burning? I read somewhere that enough sleep is a factor in weight loss.
There is indeed some research that links sleep deprivation to a greater incidence of obesity, so it does not seem illogical to conclude that sleep plays some role in properly burning fat.
There is also some other research linking sleep deprivation to hindered sports performance. There are better resources than the one I just linked on Google, but they appear to be screwing up and not loading at this time. I will update this answer when I see it working. For now, please accept the search term 'sleep deprivation athletic recovery' as a springboard for your own resource search.
From a purely logical standpoint, all of this makes a lot of sense. Sleep deprivation, in many ways, mimics alcohol consumption. Alcohol's effects on athletic performance and recovery is well known, due to the disruptions it causes in both your digestion and your nervous systems. Hormonally, a lack of sleep also taxes your adrenaline glands, which now must pump adrenaline just to keep you at base line alertness. Properly rested, you would instead be using this adrenaline to meet your athletic demands.
Finally, anecdotally, napping has been part of the training regimen for some sports for centuries. Sumo comes immediately to mind where junior wrestlers are woken up at 5AM, work hard for about 4-5 hours, then have a huge lunch and go back to sleep. While I'm not sure one would want to take weight loss advice from a sumo wrestler, I don't think anyone could argue that their musculature and fitness level is also very impressive.