If you are staying at the Sheraton Heathrow Hotel (check the name!! as there are two Sheraton Hotels near Heathrow and this advice does NOT apply to The Sheraton Skyline) or indeed at the Thistle Hotel on the Colnbrook Bypass you might like to know that if you catch the 350 Bus to Heathrow Terminal 5 from the stop opposite the Sheraton Heathrow, then it is a FREE RIDE. The buses are every 12 minutes during the week and every 20 minutes on Saturdays. The 350 bus leaves Stop 6 outside Terminal 5 at the same time intervals and it is free at least to the first stop, which is where you should get off for the Sheraton Heathrow. You should also know that the Tube (London Underground) from Terminal 5 to Terminals 1, 2, and 3 is also free. Beyond Terminals 1,2, and 3 the Tube is most definitely not free.
In other words, you can get to Terminals 1,2,3, and 5 FOR FREE from the Sheraton! You will have to pay if you use a taxi or the hotel shuttle bus (H4). They are quicker, but they are not free.
The Tube takes about 50 minutes to get from Terminal 5 to Piccadilly Circus. The Tube Line is the Piccadilly Line.