Well, when I used this method once, the police didn't come, but my neigbor wondered what was going on. That night an ice storm downed a big oak tree and it took out the street's main power line. I talked to the power company crew forman and he said it could be 8 hours plus before the power came back on so it was time to improvise. At the time I had about a dozen 20 gallon aquariums w/ poison dart frogs, some of which I was taking care of for a friend. House temp was in the high 50's when I came home (frogs needed a min of high 60s) and the frogs had buried themselves in the tank's substrate.
I stacked them like a pyramid w/ spaces in between. Put several old fashioned car mechanic's lights w/ 100 watt bulbs in the spaces, covered everything w/ moving blanckets & comforters & plugged the power strip into the inverter....hoping. The temp stabilized while the room temp declined, and then began going up. Since the house was cold I slept in the car with an egg timer set to go off about every 45 minutes so I could check things out. Luckily, no losses of adult frogs. A few juveniles perished later but unfortuantely all eggs and tads were toast (ice?). Luckily my car's a little more comfy than a 95 Geo but still, not a great night's sleep. Like I said, no cops were involved buy my neighbor knocked on the window to make sure I wasn't dead of carbon monoxide poisoning (scared the bejeepers out of me).
I plan to use it as a back up (once tested) until I can put a better solution in place on my new (on order) SW system, although at 500 peak watts I don't think it's going to run pumps plus the heater. I may need something bigger or another unit to run on a second vehicle in the event it happens again.
I once saw a device in a greenhouse catalog that dialed preprogrammed phone numbers if the temp reached a certain level. That might be nice to have and plan to look into it.