If you are going to keep the house somewhat heated I strongly recommend some type of monitoring for power outage or heating system problems. I've used a "Freeze alarm" for years with pretty good success. It uses a "pots" telephone line to call up to 3 phone numbers if the inside temp falls below a level you set it up for.
This past fall after having multiple phone system failures, I purchased a $99.00 Motorola Multisensor.
https://motorolanetwork.com/mc4000.html
This device uses a Cellular interface ($5.00 month cell charge thru ATT). to call you in the event of a low temperature situation In addition to the low temp it also gives you the following alarms
Shock Sensor (I set it sensitive enough to detect footsteps in the house)
AC power failure. The unit has a internal battery with several days backup
Flood sensor with optional water probe
Light sensor, It tells me if its daytime or night time. I suppose you could use it to monitor lights on a timer.
Relative humidity.
All this is reported via a cellular interface and the unit will send Texts, email's and voice alerts.
I've used this system thru this past winter with fantastic results. I now have redundancy for my freeze alarm and I'm not tied to having an active phone line or AC power.
One note of caution, If you are going to heat the house while you are not there, set the alarm point sufficiently high to allow a cushion before the house freezes and damages pipes. I set mine at 50 deg which I believe will afford me at least 24 hours before a hard freeze occurs, in that time I can either get a service contractor to the house or get there myself to repair any issues.
YMMV
Charlie T