In my experience, modern English adopts idioms more often than new words. "Sexual fantasy" is a common term for what you're asking about. It may sound too dry and basic to be an idiom, but remember that English is packed, filled, stuffed, and choked with synonyms. That most people say "sexual fantasy" points to it being an idiom. "Dirty thoughts" would be a close contender.

If you really want a single verb, "lust."

For sexual fantasies about somebody one's looking at, "undressing with one's eyes."