I do this journey every time I fly from Heathrow. I'd actually be entirely comfortable with a tube journey the whole way with that sort of buffer.

Whilst the nominally fastest route is Central to Holborn changing to Piccadilly, at that time of day Holborn is a zoo and it can take a long while to get onto the Piccadilly Line platform - so I'd take Circle to Gloucester Road (an unannounced transfer point, so therefore usually quieter than South Kensington) and on to Piccadilly from there. Time wise it's only slightly longer even with a smooth journey, and in reality at that time possibly 20 minutes quicker - plus the carriages are much, much less crowded.

Leaving at 4pm I'd expect to be at T3 by 5.30 latest.

The fastest - but clearly far more expensive - is, as has been said, either Circle or Hammersmith & City to Paddington, then HEX. You're probably typically looking at 45-50 minutes total.