Never really had a problem with painting MDF, be it thin or thick. I always seal it with a primer, a couple of thin-medium coats. Normal paints and painting methods work just finely after that.
What I've found CAN warp MDF is the gluing. This is especially the problem with two-piece MDF movement trays, where you glue big/long surfaces against each other. Here, weights (books etc.) are the way to go.
Then again, gluing texture on assembled MDF never warped it. It's the thin 1-2 mm sheets that may warp because of moisture. 3-4mm thick doesn't seem to warp at all.