Just been sent this:

Thank you for your recent enquiry on the Piccadilly Line service to Heathrow
Airport, which has been passed to me.

In answer to your enquiry, Terminal 4 station is expected to be closed from
January 2005 for around 20 months, to allow construction of a junction in
the area to extend the Piccadilly Line to Terminal 5.

Customers for Terminal 4 will be able to use a bus replacement service which
will be provided, running between Hatton Cross Station and Terminal 4.
Terminal 1,2,3 station will continue to operate Piccadilly Line services
throughout this closure period.

I hope that this answers your query.