Straps, rope, blankets on top, etc... Or just get a tighter fitting cooler to convert into a mash tun.
I notice that my 70qt Coleman Xtreme cooler/mash tun has a really tight fitting lid when cool/cold, but it gets looser during the mash. If I place it far enough away from the propane burner, when mashing, the fit stays tighter, longer. If I put up some kind of heat shield, it's even better. I have placed thermal shielding on the back of the cooler, as well as the lid, and typically have that facing the burner now. Works much better. I was also considering getting some straps (automotive, or for furniture moving) but haven't just yet. I'm hoping that I won't need to.
Mine doesn't have any steam escape (when I can see steam from it) even during cooler months. Just the lid seemed looser until I made the modifications.
Also, the RubberMaid cooler mash tun (10 gallon round/beverage type) doesn't have any steam escape and the lid stays nice and tight on it.