Deer will hold heat longer than a bird and will hold heat longer in hotter ambient temperatures. Feathers are very, very good insulators and cover the full bird and birds do not hold a lot of blood . I do not even consider thermal of real use finding dead birds , deer yeah you can pick up where a deer is laid but the window in time is short ( too short and too unreliable) to aid in more than easy marked fresh recoveries in my own experience.
Just about any dog is way better than £2k thermal.
I thought this one was interesting. The deer was shot late in the evening, then it laid up and died overnight, and was subsequently covered in an inch of fresh snow.
It still gave a strong thermal signature the next day.