Bats are normally nocturnal, despite some potential advantages of bein
g active during the day. A possible constraint on diurnal activity is
hyperthermia. We evaluated the hyperthermia hypothesis by constructing
a biophysical model which considered all the heat fluxes across a bat
's wing during diurnal flight and predicted a critical ambient air tem
perature (T-acrit) above which a bat would be unable to fly without ex
periencing fatal hyperthermia. Many factors had important influences o
n T-acrit, including time of day, latitude, cloud cover and foliage co
ver. Ground surface temperature and ground albedo had significant but
mutually opposed effects. Important organismal factors included body m
ass (larger bats were more susceptible to overheating), aspect ratio (
lower aspect ratios more susceptible), flight speed (slower more susce
ptible), and the albedo and transmittance of the wing membranes (darke
r more susceptible). Using the expected latitudinal variation in the e
nvironmental components we suggest hyperthermia will constrain the diu
rnal flight of large bats (c. 900 g) at about 85% of sites between 40
degrees S and 40 degrees N. For intermediate sized bats (90 g) hyperth
ermia will constrain diurnal activity at 50-60% of sites between 20 an
d 30 degrees N and degrees S but is less important around the equator
(constrained at only 10% of sites). For small bats (9 g) hyperthermia
will constrain diurnal activity at about 30-40% of sites between 20 an
d 30 degrees N and degrees S, but less than 1% of sites at the equator
. For all sizes of bats hyperthermia probably constrains flight in the
day at less than 1% of sites above 50 degrees N or degrees S.