Capsaicin binds to TRPV1 receptors, which are mammal-specific. Other animals have different proteins in this role and birds in particular are not sensitive to it. Also TVRP1 is only triggered by temperatures over 43°C, lower temperatures are sensed by other proteins.

Capsaicin isn’t just effective on mammals, it also has an effect on some fungi and insects, though mostly through metabolic disruption.

Probably a different channel that isn't triggered by capsaicin

Have you seen birds swimming in the winter? Doubt they care much about temperature. /s