Remember chickens create a lot of dust. So anything you have plugged in, in the coop will collect dust inside and out. Keep things clean. Last year I had a heater in the coop get stuck with the thermostat "on". It was about 80*F. The hens were lounging about in their bikinis.
It wasn't a fire hazard yet, but was immediately replaced. Also make sure nothing can fall on bedding or combustible stuff.
and here's one you might not have expected.... i walked in one (cold) morning and the heat lamp i had hanging in the coop was unplugged and on the ground. hum. how weird. then i noticed the burn marks all the way down one of the walls. i'm not sure how or who did what... but apparently one of those silly hens got stuck in the cord (!?!??!!?) and it kind of slid down the wall burning all the way down! yikes! thank heaven it got unplugged - i kinda like to think the rooster did it...but you know how that goes!
anyway - we now have double security on only lights that are hung!
Barn (including coop) fires are distressingly not-rare; the chances of one happening to you are small if you build, maintain and operate your coop sensibly, but it is good to be aware of the commonest causes of electrical fires in barns/coops.
They include, in no particular order:
--heaters or heatlamps falling onto combustible material such as bedding, or being mounted too close to combustible material e.g. too close to floor or wall;
--combustible material such as bedding, dust, feathers piling up or falling onto heaters or heatlamps;
--sparks from shorts due to rodents chewing wires or poorly wired connections, or from plugs that come half-unplugged and arc across the gap, igniting dust/shavings/feathers/whatever
--stuff being used that exceeds the electrical capacity of the circuit, with the result that wires heat up and set things on fire;
and (I dunno if this counts as electrical exactly) dust building up on anything mechanical and then starting a fire when the fan or whatever is run.
If you know the capacity of the circuit and are careful not to exceed it, make real sure the wiring is appropriate type and the connections are very correctly done, mount your electrical equipment safely and make real sure that combustible stuff is not allowed to pile up on or near it, you should be pretty safe. Frankly a considerable number of barn fires are things where 'you could see it coming', except -- this is important -- the person usually sort of knew it was a risk but decided that it would be ok in this case because of <whatever> or because it'd been that way for so long and nothing had happened.