I doubt that there is any way to avoid it, other than somehow getting a better ID before your return flight. (E.g. if the permanent driver's license card is being mailed to your home, and it arrives before your return flight, you could have someone pick it up and send it to you.)
TSA PreCheck will not help here. For one thing, it isn't a fully online process: after the online application, you have to make an appointment to go in person to an "enrollment center", at which you have to... show identification. You can find here an explanation of what kind of ID you would need to bring; naturally, temporary driver's licenses are not on the list. And even after you've attended your appointment (for which there may be a wait), it can take several weeks for them to finish processing the application. Unless your trip is quite long, you probably wouldn't be done before your return flight.
Also, PreCheck still requires you to show ID at security screening just like everyone else. And my guess is that they would be even more insistent on seeing proper ID from a PreCheck member: in their minds, since PreCheck member "Karen Smith" would receive a less thorough screening, it makes it that much more crucial to verify that the person standing in front of them is really Karen Smith and not some terrorist impostor trying to sneak into PreCheck.
(Yes, we all know this isn't real security, etc; please skip all the followup comments about "security theater".)