I'm not sure as to your plans in Phuket, but you really need a few days to see Bangkok right. In your boots (with your wallet) I'd try to get a morning flight from Bangkok to Phuket and just hang out at the airport through the night. You can then work off the jet lag while lounging on the beach. There are plenty of flights to the island so you shouldn't have much trouble.

Spend a few nights in Bangkok on the way out. You'll be well rested and ready to do some proper sight-seeing. Pick up your Thai souvenirs in Bangkok rather than Phuket; you'll save money.