@OP,
i am not sure of the COTS stuff, but an Arduino with appropriate sensor + wifi or ethernet wired, can be programmed for exactly what you want to do. i suspect using some sort of light sensor you can monitor the pilot light of the boiler, and if it goes dark then the Arduino would send alert and can turn on a alarm buzzer. or, perhaps a thermal couple sensor and if it goes cold the alarm is sent, etc.
if you need no-util-power monitoring then you'll need a small UPS for the Arduino power (wall wart), wifi AP, and internet access device, etc. if you want more fancy you can integrate a Verizon cell card.
past that, look to home alarm companies, those that use the Honeywell line of stuff have all sorts of sensors and what not, and, they have cell card options, all COTS stuff. my home alarm/monitoring system has additional fire detectors linked into my alarm panel, and if they go off the alarm panel sends alert via cellular to the alarm company who then dispatches the FD, and its all on batt backup. w/ a different t-stat i could link it into the alarm panel and program the t-stat to alarm on hi-lo temps.
NEST and the like are tricky, because they rely on other things like internet access, hence, it all needs to be on a UPS for it to be a good system. How stable is the Internet access, etc.