Vital signs from children seen at two emergency departments (but not admitted, so as to exclude those with serious illness) were examined to quantify the effect of temperature on heart rate (over 21000 cases) and respiratory rate (over 14000 cases).
A rule of thumb was derived showing an increase in heart rate of about 10 beats per minute for every 1 degree celcius above normal.
The relationship between temperature and respiratory rate was less easy to demonstrate because of the widening of the normal spread of respiratory rates as temperature increases. However, previous reports of an increase of 5-11 breaths per minute per degree are likely to be an over estimate; this study would suggest it is closer to 0.5-2 breaths per minute.
The authors plan further study to validate these findings.
The relationship between body temperature, heart rate and respiratory rate in children
Emerg Med J. 2009 Sep;26(9):641-3