An alternative to staying at the airport would be to stay nearby in Windsor (15 minutes away+-?). While it can be crowded in peak seasons, it shouldn't be unduly crowded at all in February. I was there twice in May (to be near my son who was a school nearby) and it was a good place to decompress after a long flight from Seattle. If I only had 1 1/2 days I think I'd rather spend it unhassled in a small town rather than spend it in London (wasting lots of time in transit, etc). Not sure if Windsor Castle is open that time of year? But if it is, and you like museums and art and history, it's a great place to ramble (I went there twice, kept noticing new things I'd missed the first time, etc.)Also, St. George's Chapel on the Castle grounds is wonderful, historic--go for a service if you're so inclined--they're usually well done and moving. Way too many sourvenir shops, but a decent regular high street. The River Thames isn't very large there---separates Windsor from the town of Eton. Picturesqe pedestrian bridge in the center. Lots of restaurants along the river. Eton College---great place to tour--see the chapel.
First time I stayed at Hart and Garter---adequate, nothing fancy. Second time I stayed at The Castle Hotel---much better. Both on the main street---some rooms have views of the Castle looming on the hill above town. There is also Sir Christopher Wren's House Hotel at the river---looked interesting, but don't know much about it.
I would think Windsor and Eton would be just about the perfect stop near LHR for such a short time. Enjoy.