Birds tend to be well insulated so when they fly at altitude in cold weather they don’t lose all their body heat.
The color it appears on infrared footage depends on the other pixels in frame. It uses dynamic ranges to map infrared values to a visible light spectrum. If the rest of the frame was ice, or you were looking up into space, a bird would probably be rendered as very warm.
If the rest of the frame is a warm ocean surface and warm wind turbines, then a flying bird may be rendered as cold relative to those pixels.
Balloons can also show up as a different temperature than the background of the frame depending on what the balloon is made of, altitude differences (ambient temp at high altitude is colder than at the surface), etc.
Could you find some videos for those cases? Would be interesting to see this in action.