I have plywood in the bed of my 39. It fits perfectly between the wheel wells, but I think this was the last year a step side bed was that narrow.
Since I do live in Arizona, it has been in there for over 15 years. I'm just about ready to replace it and I'll probably do it in T1-11 with 8" grooves this time around.
No, this is no substitute for a real bed, but since I'm not quite ready for the ground off resto, this suits me fine while I'm still hauling spare parts in the back.