+1 on above. Dropping coolant level after 1st heat/cool cycle is normal.
Gennerally the 4.6 SOHC motor will self purge the air from the cooling system after a few heat/cool cycles. If not, it almost always means there is a leak or combustion gases are entering the cooling jacket.
The DOHC and V6 OHV engines WILL OVERHEAT if the coolant refill procedures are not followed and all of the air is removed.
The DOHC is especially difficult to remove all of the air from the cooling system. The procedure is time consuming requiring multiple steps and heat/cool cycles. For that reason, the dealer will use the vacuum refilling method (saves time).
2003 GT Convertible (sold)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.