I've worked with IR systems for a number of years. And the answer is that even if the light was sitting out in the middle of the room (no tent) and no window blinds, it wouldn't be visible from the outside through FLIR with any normal house or apartment. Even window glass will block direct IR emission. The walls and roof will completely block direct IR emission.
What will be visible to an IR camera? The external temperature of your house and any heat being vented to or radiating through to the outside (like hot water pipes inside the wall, attic vents, or running dryer vents). However, one 1,000w light is not going to heat up a house to an extent that it is going to stand out to your neighbors. Venting a 1,000w directly outside... and the venting will be visible but not definitive (someone is not going to absolutely know the venting is from a grow light and not a clothes dryer, portable A/C, or something of the like).
I can't speak for the law enforcement aspect of it, but in my mind/my opinion - unless you are already under suspicion of growing, venting a 1Kw light directly outside isn't likely to get you caught in and of itself (it could be grounds for further investigation but not likely to be grounds for a warrant by itself). But your mileage will vary depending on where you live, the judges where you live, the law enforcement community, and the presence of any task forces working with your local PD. The safest thing to do is vent to an interior room, mix with A/C, and vent out of normal places (like the attic or a dryer vent) and otherwise stay out of trouble and don't tell anyone what you are doing.