Should i install a heater?

Have a small tubular heater knocking around in the garage and am thinking of installing it under the nest box (out of direct contact to the chickens)

Or is this over the top?

I have run power to the coop and installed lighting already, just thinking of giving them a bit of extra heat in the cold winter months? The heater has a low kw rating so is very economical.

Thinking of fitting under the nest box, external to the coop. And even go one further and control it via a frost stat, so that it only comes on when the temp drops below a set point.

I make sure i close the pop hole every night as the wind does tend to whip down the side of the house where the coop is situated.
Was just thinking, i have this heater spare, not doing anything, and thought it would be beneficial the chickens.

Might do it this weekend and see if they like it.

Just looked out the window and we have complete white out here! Brrr!!!

You have the same coop as me, I've just given them a thick layer of straw to help keep them warm, and partially closed the vent hole. There's another thread on here, (or it might be on the chat pages), showing a thermal image of a chicken. It shows how well they keep their heat in under the feathers. They will also snuggle up together to keep warm.

I extended my run this year to give them some more room to move whilst they are inside. They love it!

The light is for my benefit 
I dont get home until gone 7pm, so of a night i can clean them out, top up feed, water etc. It really is the best mod i have done. I also have one in the nest box.

i'd be worried about keeping them too warm and snug at night as i think they may feel the cold when they go outside during the day.

I don't think they'd need artificial heat, just lag the coup floor well with wadges of newspaper and deep bedding.  I've just done mine and its really snuggly in there, they were out, but have all gone in now to rearrang the bedding to their liking, as I never seem to do it right for them   It's quite snuggly in their, deep clean bedding, and out of the icy wind.  And we're in a really cold area, high up on the Lancs hills.  Quite a depth of snow this morning.

Also, if underfloor heating the nest box, might that encourage them to be broody?  Sure I read somewhere chucks bums need to be kept cool?  In fact I was told by someone with an Egloo that the nest box has a hole in the base for ventilation for just that reason.  Not sure I believed them!

Only thing I'm having problems with is keeping the water unfrozen.  Don't have power that far down the garden.