Chickens have a body temperature averaging around 42 C / 107 F - that's about ten degrees higher than humans. Some birds like the sombre hummingbird can reach as high as 113 F (about 15 degrees higher than humans - as cited by this study).
Warm Blooded Creatures
As @Gustavo and @Demigan point point out in their answers, warm blooded creatures can adapt to external temperature changes by generating heat automatically to counteract the cold. Furthermore, mammals have really good insulation properties (skin, fat). It should be noted that smaller creatures (birds, cats, etc) tend to have higher heart rates and respiration (breath faster), while larger creatures have slower heart rates and respiration. This likely is a factor in ideal body temperature as the faster the heart rate the more heat generated.
The key is to get heat out of you (sweat, breathing) when temperatures rise and generate heat within you when temperatures fall. In creatures with no sweat glands (like dogs), panting becomes the only method of heat dissipation and makes them more susceptible to danger at higher temperatures - not to mention their fur prevents heat loss more than less hairy animals (like humans).
So if your creature is warm-blooded, their heart rate, respiration, and sweat mechanisms would have a delayed kick-in at higher temperatures, but would kick in faster as temperatures fall.
A bit of an aside, but some animals can survive in extreme temperatures. This is a fascinating article by National Geographic which overviews how this works in some animals; it's an enlightening read which might give you ideas.