How do you attach wood slats around a fireplace without them warping?

The short answer on the gaps is yes, you defintely need some clearance. You are right to worry about the heat cycling, even if it only feels warm to the touch. Wood expands and contracts with humidity changes, and even small, repetitive changes will eventually put pressure on tight joints, especially where the board is glued and screwed into a backing panel. If you don't allow for that movement, you're setting yourself up for warping or cracking down the line later on. For vertical slats near a fireplace, even if it's not blazing hot, those daily temp swings are enough to cause issues over the course of several seasons. As for the gap size, I would recommend a small clearance, prolly something like 1/32 to 1/16 of an inch between each slat. It's not enough for the wood to warp visibly, but it allows for the minute dimensional changes that occur. Finishing both sides is critical, period. Even though these boards are thin, they act like tiny hygroscopic containers. If the back side remains unfinished and gets even a little moisture, the wood will swell unevenly, leading to cupping or twist. Since you are using maple, it's a stable wood, but we want to avoid any unexpected movement.

For the end cuts, since they are floor to ceiling, they definitely need attention. If they are bare maple ending abruptly against the ceiling trim, it looks unfinished and that end grain is prone to drying out and cracking. You should absolutely finish those exposed ends using a grain-filling product or by applying the same protective oil or stain used on the face. This seals the end grain against moisture. A simple method is to use a high-quality wood filler for the very ends, sand it smooth, and then run the finish over it to integrate it perfectly. It makes a huge difference in both appearance and longevity.

On past projects I've done, the only thing that caused gaps to open up wasn't the heat, but inconsistent finishing. When one board was sealed well and another wasn't, the sealed one would shrink at a different rate than the exposed one, leading to separation. If you nail the finishing process and leave adequate room for movement, those features hold up very well for years.

I've observed that when working with these thin, elongated pieces affixed to a substrate, the type of adhesive chosen for the bond is just as important as the allowance for dimensional variation. Relying solely on mechanical fasteners can sometimes introduce torque during the expansion and contraction cycles wich may compromise the integrity of the joint over time. A high quality flexible contact cement, applied judiciously to all contact surfaces prior to securing the boards, tends to mitigate this stress significantly.

This thread is really helpful since I am doing a similar project but using thicker wood for a mantel rather than thin slats. I am working with some older oak pieces and I’m mostly concerned about how the movement from humidity affects the overall bond since the wood is much bulkier. I am not sure if the same glue and screw method used on the backing panel would be strong enough, or if I should be thinking about a kind of bracket system to handle the stress. It feels like the attachment method might be where I mess up the most.