I'd have taken a hotel for the night if not at LHR itself then somewhere pretty damn close, the Holiday Inn M4/J4 was OK, a lovely quaint little English pub right outside the gate ... But budget travellers and all that!
But, as others have suggested, to get to BKK there were connection options from NQY, EXT, BRS etc. thus no need to travel all the way to the Metropolis, particularly at 3.30am of a morning.