Like last weekend, there's no service on the Piccadilly line from
Hammersmith to either Osterley or Uxbridge.

Whilst Picc trains are running between Osterley to Heathrow, LU is
thankfully not expecting passengers to or from Heathrow to change from
tube train to replacement bus then back onto tube train, and so are
running fast replacement bus services to Heathrow.

(The days of being able to jump on HEx with an LU ticket or Oyster in
these situations are sadly no more - one assumes TfL turned down HEx's
kind request to cross their palm with silver, or platinum more like.)

It's how they're doing this bustitution that's interesting, as it
depends on which direction you're travelling in:
http://www.tfl.gov.uk/tfl/livetravelnews/realtime/track.aspx?offset=weekend

Heading *to Heathrow*, the express buses to the airport (service B to
T1&3, service C to T4 and T5) leave from Gunnersbury station. Those
turfed off the Piccadilly at Hammersmith should find an easy
cross-platform interchange to the District to get to Gunnersbury.

Meanwhile *from Heathrow* the express buses (both service B and C)
terminate at Hammersmith, not Gunnersbury.

Presumably this separation of departure and arrival points works better
from the perspective of dealing with expected passenger volumes, and the
road congestion implications of having lots of buses trying to set down
and then pick up passengers. I'm guessing there might be a queue of
buses somewhere near Gunnersbury that have just come from dropping pax
off at Hammersmith, and can be made to wait so as to regulate the
services heading back to Heathrow.

That said, I imagine that however good the information given at the
Heathrow tube stations, there'll still be a fair number of air arrivees
getting as far as Osterley on the tube before then finding themselves
and their baggage on the all-stations bustitution service A from
Osterley, which runs to Turnham Green (thence District line to get
further east into town).