I have dealt with this for the past 2 winters, the metal water pail with the heater is great, I have the sealed oil filled radiator and made a cage for it from chicken wire that keeps all creatures about 8 inches from it and the whole aviary is on a thermostat switch. In fact I just built a second room onto aviary and added second heater unit for my new Silkies.
Parakeets' cage has an electric perch that keeps warm and all nesting boxes have the electric mats under them. The whole kit and caboodle runs off one power strip from extension cord to my garage about 10 feet away, no open wires or plugs can be accessed by birds.
Last thing I added was a comfortable chair so I can hide in there with my birds and read during those cold winter mornings.....(need to teach birds to make coffee)