Some will... some won't...
Humanity has this very same problem — it's just masked by sapience, cultural experience, and time.
There are articles aplenty that demonstrate that the human female experiences estrus, "a regularly recurrent state of sexual receptivity during which the female of most mammals will accept the male and is capable of conceiving." For example:
In humans, signs of sexual interest aren’t nearly so obvious. The male of the species generally doesn’t broadcast his constant readiness for sex, and during her window of fertility at ovulation, the female doesn’t display any outward signs. Some biologists and anthropologists have theorized that this “loss of estrus” in people makes us less driven by sex hormones than other animals.
But according to a steady stream of new studies by evolutionary and biological psychologists, that may not be the case. This research indicates that the hormonal changes of a woman’s monthly cycle may be more powerful than we’ve ever conceived — compelling women to advertise when they’re ovulating, and men to notice. Although women aren’t showing off swellings, yowling or spraying, studies suggest they may dress more provocatively, flirt more, and possibly become more sexually excitable, for roughly six days mid-cycle, before and after ovulation. They even show minuscule shifts in voice pitch, scent and skin tone, some studies suggest.
These changes are not lost on men, whose own hormones and mating behavior respond to a woman’s cues, as well as how the woman treats them, says Jon Maner, PhD, a hormones researcher and associate professor of psychology at Florida State University. To illustrate: In one of his studies, men actually inched closer to a woman — and mimicked her gestures more — when she was ovulating. (Source)
Your creatures will develop the same behaviors. The act of training a sapient creature (both intellectually and behaviorally, both academically and culturally) has the effect of refining the mating process. In other words...
It becomes more complex, more subtle, and more susceptible to intelligent judgement.
Generally speaking, human females during estrus don't parade around hunting for sex and the males aren't parading around...
Actually, they are. And that's why the studies are appearing. The "biological clock" that drives the male and female of our species is very much part of what drives the way we dress, the way we act, etc., but it's muddied (for lack of a better word) by the need to go to work at 6:00 a.m. and the expectations of clients/customers and the need to pay bills, shop for food, etc. Intelligent creatures have very complex lives, and that complexity gets all wound up in the genetic drive to procreate.
So, yes, your sapient animals will experience estrus... a very complex estrus
So why did I say "some will... some won't...?"
Because a byproduct of that very complex mating process (not the sole byproduct... It's really important that you understand what I'm saying) is that it's a component of sexual crime. Not the only component (do NOT accuse me of suggesting that women get raped simply because of estrus. It's NOT that simple!). So, why bring it up?
Because your sapient creatures will have similar (if not the same) problems within their society. The rules of the animal kingdom are much simpler because "no" literally doesn't come with the threat of police action or a lawsuit. In the animal kingdom, males do betimes rob other males of their females. Humans call that everything from "having an affair" to "rape."
My point is, I expect your creatures will have the same complex "how do you find a decent person at a bar?" problems that humans have, based on the nature of their own societal, educational, philosophical, and estrus rules.
And just to make this really complex, among them will be people who for reasons varying from physiological to religious choose to be celibate — regardless what a million years of evolution is telling the body to do.