I've got a 2005, so the software may be different for the older bikes, but on the basic settings window, you can change the "Initial Fuel Pulse" and the "Cranking Fuel" to eliminate the starting problems you are talking about.
The "Initial Fuel Pulse" determines how much fuel is sprayed by the injectors when the key is first turned on.
The "Cranking Fuel" will lean or richen the cranking fuel mixture.
After a little experimentation with these settings, Penelope explodes into life on the first hit of the starter button, from 25 - 105 degree weather, or after sitting in the garage for 5 months all winter. It doesn't matter if she's ice cold or only been shut down a few minutes.
So check the manual for your T-Max version and try some minor changes to see if it helps.
2005 FLTRI Black Cherry, 95" Big Bore, Thundermax w/Auto Tune, V&H Dresser Duals w/Klock Werks SS, Andrews 26 Cams, SE Stage 1 intake, SE OD/6 Speed, Wards FCS cooling fans, Krome Werks Stretch Heritage +2 bars, Progressive Monotubes, 444's, & Touring Link, Michelin Commander II's, 14.5" Madstad, Lowers with Classic Motorcycle Vents, detachable King Tour Pack, Daymakers