I've never known, seen, or heard of anybody (I could verify) getting permanently banned for appealing a temporary ban. That's out of many such instances in our family, friends, and our Runescape group. I did see one person get permanently banned for offenses that occured just after the offense that led to the temporary ban (during the wait time before the offense and Jagex looking at the offense), and the perm ban happened while he was appealing the temporary, but the ban was clearly stated to be for the later offenses, the last of which was RWT.
You an appeal it, but most 10 day ban appeals are denied. There's nothing to lose, though.
EDIT: I've heard of permanent mutes for people who appealed a temporary mute, so if that's what you got, you might want to wait it out.