Although the film is quite coy and cuts away from the actual naughtiness, we're left under no illusions that they had (ahem) physical relations, that being the only known way to cure a Vulcan's 'pon farr' urges.
Spock reached up and gently touched her cheek. His fingers followed the upward stroke of her eyebrow, then curved down to caress her temple, as Saavik met the gaze of his gold-flecked brown eyes.
[several hours later later]
Saavik smoothed Spock's tangled hair. The fever had broken, the compulsion had left him. He slept, and he would live. She wondered if she had done him a kindness by saving his life. He was still completely vulnerable to the convulsions of Genesis, which would continue to torture him.
Star Trek: The Search for Spock - Official Novelisation
He is more in control now... intense. His eyes turn and lock on hers. Hands touching, they move together until their faces are brushing... and their fingers embrace.
INT. CAVE - GENESIS - CLOSE - THE YOUNG SPOCK:
Morning light is streaming in. His eyes are closed, he breathes calmly. A hand, Saavik's, ENTERS SHOT, to sooth his brow and smooth his matted hair.
Star Trek 3 - Script