If you heat the whole shed, how are you going to handle ventilation......
.....without spending ridiculous amounts of money on the heat?
If you heat just above freezing temps, it's really not that hard to balance the two, nor is it that costly... During mild winter months, my heating bill on a 1800 sq/ft coop is about $100/month... During daylight hours on mild winter days the furnace hardly runs at all, I had several weeks last winter where I used only about 5 gallons of propane a week... During extreme cold, colder nights or windy weather I damper down the venting temporarily, to help retain heat...
Back to the OP, for a small coop, I highly recommend flat radiant heaters, in a 'heating box' and of course wire it properly, no extension cords or exposed wires...
If you use 'pig blankets' aka livestock nursing pads you can avoid worrying about a thematically control and for the most part negate any fire risk or burns as they only get about 20°F above ambient temps...
This is my idea of a side view of a 'heating box' perch for the peas, make it just big enough for the peas to navigate and use, in addition to pig blankets on the back they can also be included on the sides... This box would be installed inside the coop replacing summer perching location...
In the above you can see the radiant heater in red spaced off the rear (and possibly side walls) by 1" or 2" spacer blocks, allowing air flow over both sides.... Spaced off in front of that (in gray) is chicken wire to prevent the bird from physically laying against the heater... Even though it technically never would get to a burn temp it's best to avoid direct contact IMO... The peas will naturally roost head out so they get 'fresh' air, while the roof design and semi enclosed box traps warm air directly around them...
May I asked did you get the java greens locally? I have been on a casual lookout for some in the local area and have not had much success in finding any...