I'm thinking of installing a plastic cage over the thermostat
What are you thinking of doing to the thermostat?
I'm thinking of installing a cage over my thermostat, so my roommates can't change the temperature.
You shouldn't stop overs from being comfortable. Maybe talk it over and set some rules on the degrees the house should be at.
Nah, there's no point talking.
I believe having a house discussion about the thermostat would really help your issue. When you share a house with roommates it's important that everyone feels included in decisions about the rules of the house.