Thermostatic Control of Simple Apartment Heater
NOT an electric heater - a hot-water heater with an electric fan, connected to a central source of hot water (which might be under control of a thermostat not local to the Fan Coil Unit.) It is not inherently hazardous to leave such a unit turned on 24 hours a day.

Would be a fairly simple/inexpensive "robotics" project to have a temperature sensor and a servo or stepper motor that connected to the dial, which would not require any "landlord irritating" attempts to modify the internals of the heat unit. Landlords are not generally thrilled with tenants who modify things the landlord owns, so don't go there.