To the OP:
I am a tanker, and per your request, we'll do a little edification.
The M1 Abrams platform, in all its iterations, are capable of firing accurately on the move, even at full throttle. All systems, M1A1 variant included, have a thermal sight for the gunner. The M1A2 (apparently not a suspect in your issue) has a FLIR system, an advanced form of IR targetry, in addition to the thermal sight intrinsically included in the Abrams fire control system.
Considering that your vehicle had manuevered to a position to overwatch their egress from the FOB, it would intrinsically be warm, if not goddamned hot. Furthermore, it would take hours for the heat to dissipate from a metal chassis and armor system. Turning your engine off would simply not cut it. Even being in defilade (hiding in a ditch, for example) would not prevent the opponent from spotting you with thermals, especially considering that armored vehicle tactics involve scanning multiple sectors. Any exposed metal pieces, even coated in the CARC (chemical and acid resistant coating) paints that NATO and Russian forces (and other former ComBlok countries) are known to use, do not dissipate heat well enough to eliminate retained heat from hydraulics or engine activity. Furthermore, the tank commander is also responsible for calling targets and scanning the area for potential risks and targets of opportunity.
Perhaps that will shed a little bit of light on the situation for you. Thanks for your time.