What happened during the adult scene in "300: Rise of an Empire"?

To more directly sum up what you're looking for:

Artemisia invites Themistocles to her ship after he bests two of her generals in battle. The plan is to get him to join her so she can destroy Greece.

Themistocles agrees to board her ship. He boards her ship.

Artemisia tells Themistocles she knows he has no reinforcements coming in time for the next battle, and that she can keep throwing ships and resources at him for months on end. She offers to let Themistocles join her at her side.

They have sex. The dialog you're missing here is a lot of panting and screaming as the two throw one another around the room.

Themistocles refuses her offer.

Artemisia throws him off her ship.

There is literally no dialog you're missing that's key to the plot or character development. They have violent sex, and that's pretty much it. A copy of the script will likely not be available as the movie is less than a week old on theaters, but again, it would be pointless.

The key thing to remember with Artemisia is that she absolutely despises the Greeks. She doesn't just hate them, she wants them eradicated from the world. This is due to her people being ransacked by Greeks in her childhood, with her being taken captive and used as a child sex slave for years until her usefulness to her captors wore thin and they abandoned her, leaving her for dead in the streets.

However, she knows talent when she sees it, and always seeks an opportune moment.

She invited Themistocles to her ship in the hopes of seducing him not only with her body, but with the potential for power. Themistocles knows how strong the Persian forces are, and Artemsia attempts to bring this to light ("I can throw forces at you for months...") while offering him a place by her side and all the power he could ever dream of. The two engage in sex, but when Themistocles finishes and refuses her offer, and renews her vow to eradicate the Greeks. She tells her guard to, "Get this filth out of my sight," because she views all Greeks as filth, and is attempting to insult him for having just taken advantage of her.

Whether Themistocles let down his guard in the heat of passion, or knew what he was doing in an attempt to enrage Artemisia isn't really the point of the scene. What is, is that Artemisia is used by the Greeks yet again. She was hopeful to lure him to her side, with all his knowledge of the Greek forces and brilliant military tactics, but instead was used for sex, rejected, and now yet another Greek gets to return to his people and brag about how they used her. Themistocles might have been trying to play mind games with her in an effort to throw off her own sense of strategy, but again, the point was to show that Artemisia gets used one final time, and believing Themistocles to be dead at the end of the next battle, returns to Xerxes believing she has won, only to be killed by Themistocles in a later battle.

I've not seen the movie and the script hasn't been made available online yet, but quoting from the Wikipedia page:

Impressed with Themistocles' skills, Artemisia has him brought onto her ship, where they have sex. She offers him a place in her army, but he refuses, causing her to swear revenge.

So effectively she seduced him, he allowed her, but he refused to join her army which is what led to her throwing him out.