The cheapest way in. Nothing listed is quicker.
Piccadilly line
Piccadilly · Transport for LondonPickup, hours & luggage
Boards at. Underground stations at Terminals 2 & 3, Terminal 4 and Terminal 5
The same £5.90 on Oyster or a contactless card, from any Heathrow terminal, to any Zone 1 station, at any hour — TfL offers no off-peak fare on this journey at all. A paper single is £7.00. It counts towards the daily cap, which the Express does not.
Luggage. No stated limit, but it is a tube train and the Piccadilly line has no racks.
Hours. The airport states trains run between 05:00 and 23:30. On Friday and Saturday nights the Night Tube runs through, but TfL's timetable says it serves "Heathrow Terminal 5 (excluding Heathrow Terminal 4)" — so Terminal 4 has no night service on any night.