You could also get the Heathrow Connect service which is slightly slower & cheaper.

But unless either your hotel is in the Paddington area or someone else is paying I wouldn't bother with the HE / HC as it's almost as quick (and a lot cheaper) to use the Tube even though you'll have to get a bus to the Tube from T4.

Of course as you are arriving on a Piccadilly Line closed weekend, you could buy a Tube pass & get on the HE / HC.