Try holding your hand as close to the lamp as a chicken's head is likely to be. Hold it there and see how hot it feels after a while. A 250w might be too much in one spot in that small of a space, but a pair of 100's or a string of 40's would work better. The radiant heat might not warm the air, but warm air is only one "heat" effect that we perceive. The other is the heat that we radiate and the radiated heat we receive from other surfaces. That's one of the reasons why you feel cold sometimes even though the thermostat is keeping the house at 72 degrees - your radiated heat is being absorbed by the cold exterior walls, more than the walls radiating heat back at you.
Half-inch plywood has an R-factor of about 0.6, by the way. If you want the heat in the coop to stay in the coop, any insulation is better than none. I used foil-faced foam in mine, because the foil reflects radiated heat back. That effect is in addition to the insulation's resistance to conducting ambient air warmth. I paneled over the insulation with melamine-faced masonite to keep the chickens from eating the insulation and to make it easier to clean.