I have a similar situation to you. I have a shop that is unheated and a hose bib that supplies water to my animals. On the inside of the shop, the bib is under a sink and there is a light bulb to keep the water supply from freezing. But, the bulb burns out periodically (maybe once a year). I turn it on when it gets cold enough in fall and off in the spring so it's burning away for up to 6 months. I used to have a single 60W but it was too much heat and burned out more often. I swapped to an appliance 40W which did better but still burned out eventually.
I had intended on installing some kind of monitor setup to determine if the temperature was too low and alert me to it. While that would have worked, it would not keep the heat on if the bulb failed. The next best option would have been to install a reptile tank heater (think ceramic bulb that produces no visible light). The problem with that for me was that it produced no light so I couldn't visually see that it was working if I looked under the cabinet.
So, my solution in the end was simple. I installed a bulb y-adapter and have 2 25W appliance bulbs plugged in. It's very unlikely both will fail at once. If one fails, the other provides enough heat to keep things working ok. 2 bulbs doesn't over heat the enclosure. And I have a visual indication that things are 100%, 50%, 0% working. No monitoring remotely, but it's reliable enough that I can go a week or two without worrying about it in a worst case scenario which I could not guarantee with a temperature monitor or ceramic heater situation.
