Most, but not all, mosquito species are crepuscular and thereby feed at dawn and dusk and for a few hours into the night. However, there a few of the more aggressive species will 'be on the hunt for a feed' at any time of day!
The term crepuscular characterizes creatures that are most active primarily during twilight/half-light (just after dawn/immediately before dusk), as opposed to diurnal (daylight active) or nocturnal (darkness active).
You will note that I have used the terms light or dark or half-light as opposed to day or night rather than use the terms daytime/night-time as it is primarily the light (and associated heat) that affects their activity levels. So a crepuscular creature could also be active during a very cloudy overcast day or on a very bright moonlit night.
Additionally, mosquitoes are ectothermic (cold-blooded) so they 'prefer' warmth but, conversely, they are also prone to overheating or even drying out in extreme direct sunlight conditions.
Finally, for now, mosquitoes also use their thermal and odour receptors to home in on their hosts. These two 'feed-seeking weapons' in their armoury are much more efficient during the cooler and sometimes more humid, conditions prevalent after darkness descends.
As an aside, there have been several ongoing scientific experiments, such as here, to investigate/research the possibility of disrupting these powerful mosquito receptors as a means of mosquito bite prevention.
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