Are you in the U.S.? If so, they need a warrant FIRST to thermally image your home. They can't peek inside your home with a thermal imager and use what they see to get a warrant; they have to have the warrant first. The Supreme Court has ruled on this already and it is the law of the land now: thermally imaging your home IN AND OF ITSELF constitutes a search and is thus illegal without first obtaining a warrant to do so.

And if they ALREADY have a warrant, then there's no point in thermally imaging your home at all; it's far cheaper to send two or three squad cars to your home and tear it apart. Probably more fun for the cops that way too.

There was just a Law and Order that touched on this. They used thermal imaging on a mosque (the episode was related to terrorism), and because they used the thermal imaging before they got a warrant, any evidence that was obtained had to be thrown out.