Exactly how steamy is this story?
NC-17
Let's put it this way: when a basic element in the plot hinges on Enkidu having sex with a temple-prostitute, you're just not getting away without a little canoodling.
That said, the sex rating of The Epic of Gilgamesh depends a bit on what translation you're using. For example, don't let your grandmother catch you reading Stephen Mitchell's version (entitled simply Gilgamesh); we think that one is more like XXX than NC-17.
If you're reading some of the older translations, you may have to use your imagination a bit, but you still shouldn't have too much trouble detecting the steaminess. In the Kovacs translation that we at Shmoop are using, for example, Shamhat is told to perform "the task of womankind" (1.167) for Enkidu. She does this by "unclutch[ing] her bosom" and "expos[ing] her sex" (1.170). Apparently, this works because Enkidu ends up with an erection lasting seven nights.
Hey, we warned you.