Although you are enquiring about remaining airside, which as indicated, you can do, transiting through the Flight Connections Centre can be a real problem at certain times of the day, especially when the big North Atlantic flights arrive in during the early and mid morning. The problem is that all inbound passengers from non-UK destinations must pass through security and this is real slow at bad times. I've often exited landside and re-entered through the front of a terminal. Customs at LHR is not bad and as you will inbound on a European flight you can exit through the BLUE channel very quickly. It's a 10-12 minute walk from T2 to T3 (the best bet is to follow the underground route so you don't get lost on the LHR road system!).

If you do exit to landside (even if your bags are checked through) make sure you get issued with your boarding pass for entry back into T3. You can then spend a few hours in London. Either jump on the Heathrow Express (expensive!) and visit Oxford Street for some shopping or possibly get the Piccadilly Line underground to South Kensington and visit the Science Museum, Natural History Museum or the Victoria and Albert Museum. Bets hanging around LHR (unless you've got lounge access).