Desk with walnut veneer warped. How can I repair this without removing the veneer?

That's how I would handle it. Using a pin to poke holes in the veneer to help it lay flat and a razor blade to cut small slits to allow the glue to get under the veneer. Next I would cut a piece of plywood the same size as the end panel and also cut a piece of wax paper to put in between the plywood and the desk, so when the glue if any comes oozing out the plywood won't end up glued to the desk, then clamp it up.

I've done quite a bit of repair work on furniture...the first thing I'd have to ask is, how bad is the warp? Do you mean there is some warped veneer, or that the core the veneer is adhered to is warped also?

If the core material is warped, then you'll want to address that problem before tackling the veneer itself. Keep in mind, you may have a problem with some core swelling too, which will affect the finished look, even if you could do a perfect repair job re-gluing the veneer.

As for the veneer itself, yes, you can steam it to make it pliable, and glue it back down. I would use at least a 3/4" piece of plywood, perhaps even 2 layers of it, along with a layer on the backside of the panel, if needed, to form a gluing clamp. I would suggest using 2x4's to actually clamp to, putting a very slight radius on the side facing the plywood....this will create pressure at the center of the boards, where you might find it difficult to actually reach with a clamp. This method can be used to clamp very large pieces when necessary. Lay wax paper between the desk panel and anything you are putting on it, while gluing, to keep the glue from sticking to your clamp parts.

I would recommend Titebond II wood glue for a project like this.

Take your time while steaming the veneer, and check to see if you can get it to lay flat, and cover the gaps. You may find it necessary to slice the veneer with a sharp razor to get it to lay flat, and to help spread it across any gaps. (Small gaps are easier to hide with finish, than large gaps.)

You may find it easier to repair this a smaller section at a time, too, rather than all at once.

Feel free to send photos of the desk, and I may be able to offer more specific advice on how to repair it, or how to go about correcting a warped panel.

Worst case scenario, you can purchase new walnut veneer from places like Rockler's (rockler.com), and either go over the old panel, or create a new one entirely, depending on how much damage there is. If the core itself is swollen, it may be easier to create a new panel. Sanding a swollen core down would require sanding through the veneer a considerable amount, and would best be done by a wide-belt sanding machine. If you don't have a wood shop nearby with one of those machines, it'd be faster and easier to create a new panel.

Have Fun