The onset of heat cycles and the duration of the cycle varies greatly between each species, breed, and individual animal. Please see the Dog Estrus FAQ and Cat Estrus FAQ for canine and feline-specific information. Please see the Pregnancy and Reproduction section for other species-specific information.
The term estrus is also spelled oestrus, from the Latin meaning of "frenzy, gadfly". The gadfly, or warble fly, belongs to the family Oestridae. Apparently, the buzzing from this insect would drive herds of cattle into a frenzy.1.
From the Online Etymology Dictionary: Earliest English sense is of "frenzied passion;" first attested 1890 with meaning "rut in animals, heat."2
References:
1Oestridae: explanation and drawing of the gadfly, from Reproduction in Mammals
By Colin Russell Austin, Roger Valentine Short.
2"estrus" Online Etymology Dictionary. Douglas Harper, Historian. 07 Mar. 2008. <Dictionary.com http://dictionary.reference.com/browse/estrus>.
