Bats are normally nocturnal, despite some potential advantages of being 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 temperature ( (T_{\text {acrit }}) ) above which a bat would be unable to fly without experiencing fatal hyperthermia. Many factors had important influences on (T_{\text {acril }}), including time of day, latitude, cloud cover and foliage cover. Ground surface temperature and ground albedo had significant but mutually opposed effects. Important organismal factors included body mass (larger bats were more susceptible to overheating), aspect ratio (lower aspect ratios more susceptible), flight speed (slower more susceptible), and the albedo and transmittance of the wing membranes (darker more susceptible). Using the expected latitudinal variation in the environmental components we suggest hyperthermia will constrain the diurnal flight of large bats (c. (900 \mathrm{~g}) ) at about (85 %) of sites between (40^{\circ} \mathrm{S}) and (40^{\circ} \mathrm{N}). For intermediate sized bats ((90 \mathrm{~g})) hyperthermia will constrain diurnal activity at (50-60 %) of sites between 20 and (30^{\circ} \mathrm{N}) and ({ }^{\circ} \mathrm{S}) but is less important around the equator (constrained at only (10 %) of sites). For small bats ( (9 \mathrm{~g}) ) hyperthermia will constrain diurnal activity at about (30-40 %) of sites between 20 and (30^{\circ} \mathrm{N}) and ({ }^{\circ} \mathrm{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^{\circ} \mathrm{N}) or ({ }^{\circ} \mathrm{S}).