All mine are pine, if the 'box' is built properly (paying attention to which way the grain is running) then warping shouldn't be an issue, the heat shouldn't be enough to warp it.
Virides is spot on, a couple of coats of varnish is enough to seal the timber. You can stain it if you want to, use silicone at the joins to stop moisture getting into the joins.
Never use raw timber inside the box, urine (moisture) will soak into it and STINK