Oh, my. 7 hours at Heathrow sounds like my personal version of hell, so I definitely vote for heading into the city! It might be tight because Heathrow is quite far out, but you should be able to get some sightseeing or shopping in.
The Heathrow Express will deliver you at Paddington Station, which has 4 Underground lines. Would you prefer to do shopping, or sightseeing? You're close to Hyde Park there if you fancy a walk in the fresh air, or you could jump on the tube to High Street Kensington- lots of shopping, and a nice part of town to look around.