For a newer study, I've found a study that:
They concluded their meta-analysis, and two experiments they carried out, with:
However, men were more liberal in their choice in either condition, compared to the female subjects.
First, they show results of Clark and Hatfield of 1989 (brought in the other answer), summarised as:
In their study, four male and five female psychology students approached a total of 96 opposite-sex subjects at Florida State University. After a standard introduction, ‘‘I have been noticing you around campus. I find you to be very attractive,’’ the experimenter’s confederates asked one of three questions randomly: ‘‘Would you go out with me tonight?’’,‘‘Would you come over to my apartment tonight?’’ or ‘‘Would you go to bed with me tonight?’’ Men and women were equally likely to consent to a date, but men were significantly more likely to agree to the apartment or casual sex offers. No female participant agreed to having casual sex.
The aggregated results are:

Cumulative results of previous studies
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Consent rate Date Apartment Sex
========================================================
Women 31% (44/144) 18% (34/186) 1% (2/178)
Men 37% (46/128) 57% (102/178) 58% (91/158)
Moreover, they created their own experiment:
In total, 281 subjects (119 female, 162 male) were approached in a medium sized town in the south-west of Germany (about 200,000 inhabitants) on a university campus or in student clubs. All subjects were approached between June and July 2013. On campus, subjects were approached on sunny weekdays between 10 am and 6 pm and in the night clubs between 10 pm and 4 am.
They obtained the following results:

Consent rate by relationship status
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Consent rate Campus Party
Date Sex Date Sex
================================================================================
Not in a relationship (N=130)
Women 50% (7/14) 0% (0/10) 30% (4/12) 6% (1/15)
Men 73% (11/15) 36% (4/11) 96% (26/27) 65% (17/26)
In a relationship (N=137)
Women 5% (1/19) 0% (0/17) 26% (4/15) 0% (0/10)
Men 8% (2/26) 4% (1/25) 30% (4/12) 16% (2/12)
Total (N=267)
Women 24% (8/33) 0% (0/28) 30% (8/27) 4% (1/25)
Men 32% (13/41) 14% (5/36) 77% (30/39) 50% (19/38)
In an experiment based on pictures shown on a computer, the differences were significantly smaller (yet still with significantly more men interested in casual sex):
Subjects were seated in front of a laptop and had the opportunity to ask questions. The experimenter also explained to them that they could withdraw their consent to the experiment at any time. They then were presented with 10 pictures of people of the opposite sex in a random order. For each picture, they were asked how attractive they found the person and if they wanted to have a date or sex with them, respectively. During the testing, subjects were left alone in the room, with a researcher outside the door so subjects could ask questions any time. After finishing the testing, subjects completed a questionnaire. At that point subjects still believed they would meet the people they had chosen from the pictures.

In another study by Terri D. Conley, Perceived Proposer Personality Characteristics and Gender Differences in Acceptance of Casual Sex Offers (2011), summarized in Casual Sex: Are Men and Women So Different?, they considered an offer by their best friend, and in another - by a famous celebrity.
Conley (2011) conducted a second study that asked participants to consider whether or not they would accept a casual sex proposition from their best friend of the opposite sex. Initially, it appeared that women were less likely than men to accept such an offer. However, when controlling for perceived sexual capabilities of the partner, women accepted the propositions just as often as men.
In the celebrity context there is little difference (though, I admit it does not fit the "average man/woman" criterion from the original question):
Conley (2011) also tested whether women would be more willing to accept casual sex with an attractive celebrity than with an unattractive celebrity. Intriguingly, women were just as likely to say “yes” to Johnny Depp and “no” to Donald Trump as men were to say “yes” to Angelina Jolie and “no” to Roseanne Barr.