Do not think so. Theoretically it should be the same or very similar to the body temperature. There will be a limit for the body to cope with the cold air or the body starts to have hypothermia.
Measuring exhaled breath temperature is an exhiting and unrecognized field in asthma research.
There is a significant difference in core temperature vs exhaled breath temperature. I recommend Popov´s work on Respir Med 2007:101 and the various Paredi´s articles on AJRCCM 2002;165:181-84 -ERJ 2003;439 and the ERS journal "Breath" Nº of march 2012 where there is a very comprehensive paper on the subject
I think it is not so because the humidified expired air passes through the dead space and the temperature is also mixed with relatively cool air than the core temperature.