From what I understand about thermal imaging, it depends on what they are using. If they are using the older technology then they can only see the heat escaping from the house, but the newer technology then they can see into the house and yes they can see it. No Mylar will not help as it is not a thermal barrier. There are different product on the market to help you though. I can't remember the name, but there are a lot of wall coverings that will trap the heat and block the ghetto bird above. As far as 2 X 1000W lights that is a alot of power draw, I know the general rule of thumb for not getting caught is no more than 1 X 1000W light. I can reccomend you to switch to LED lights. I've switched over to LEDs and yes they do work well. I use 1 X 120W and 1X 300W lights from a Canadian company called glow Dyynamics. I'm very happy with them but think the quad band LEDs would be better. If gogin with the LEDs get the quad band lights if you can they are better. I got these because I live in Canada and don't like shipping big products like that over the border, I just don't trust those that run the country. Also get at least the 1W LEDs as they are better unless you can afford to get the 2W version. I would really recomend the Stealth Grow 600W LEDs. They look extremelly impressive, but they are extremelly $$$. They give you 600W of LED power consuming 385W of power. That is like both your lights combined. The theory is that the HPS lights give only 30% usable light and 70% wasted light where the LEDs give 100% usable light allowing you to use less power with similar results. My 120W I put up againt my friends 400W HPS and I can get a larger harvest, My 300W is crazy and his 400W HPS can't hold a candle to it. If you switch lets say to either 2 X 300W LEDs which equvalent to your 2 X 1000W lights you save 1400W of power consumption. Well under the radar and 90% less heat. Don't buy the cheap LEDs though you will be disapointed, make sure they are good quality. The 600W stealth grow solves the penetration problem people complain about using LEDs but the 300W (1w bulbs) work great. even if you get a lower yield they money you save on power and the safety you gain can be worth it.
Hope this helps you a bit. Good Luck Happy growing.