Need recommendations for monitoring vacant home

[Nathan Gesner]

I am looking for a device that can monitor a vacant home. My vacation rental is in a remote area and I may go weeks without visiting it. I need to be alerted when the temperature drops, there's a water leak, or if the electricity goes out. I need something that works on a cellular system because a power outage would obviously kill my wireless internet. I would appreciate any suggestions you may have.

P.S. I do not need a security camera or alarm system. The previous owner never locked the doors in almost 40 years and never had a break-in.