I usually have only 3-4 hours. I use the public/pay shower facilities, change clothes, have a nice quite meal somewhere, do some window shopping, hang out and read British tabloids in various waiting areas. World class people watching at Heathrow. Maybe not for everyone, but I am a nervous traveler and would not be able to enjoy trying to squeeze in a plan that might not get me back to my ongoing flight. Paying for day passes at airline lounges or even an airport hotel would be something I'd also consider.

Cymbeline, why would you want to go to Osterley? I used to live there, but I can't for the life of me imagine why anyone would want to make a special trip there.

I'd imagine he means Osterley Park - and the gardens there would make a great respite. The logistics aren't too bad since it is less than a mile from the tube station on the Piccadilly line - maybe only .5 mile-ish.