Steve is making good points. Moister will swell that wood no mater what. If my memory serves me right, most saunas I've seen are made of cedar and I think the panels are not one solid piece of wood. If I were to attempt your project, I would cut tongue and groves into the sides of 1X4 cedar boards and assemble the panel into the frame without glue... let them ride in the frame. Do leave that 1/4 inch space in the sides and maybe 1/8 inch in the vertical. Of course this is going to make the door loose so do look into space balls to reduce the rattle everytime the door is closed.
I'm not sure how much experience you have with woodworking, but to explain a couple of basics (in case you don't already know), wood will only move across the grain, not lengthwise. The space balls are tiny rubber balls inserted into the door frame groves. You can purchase them at a Rockler store... I would think Woodcraft stores also carry them.