Making Wood Stoves Safe for Pets

We have always had a cast iron stove and have had many different cats... mostly they figure it out on their own safely it seems.  
There are a couple of mild exceptions though:
One cat we used to have jumped up on the hot cast-iron woodstove once - and ricocheted right off!  Mild paw burns that healed.
His sister sometimes snuggles up almost right against the front of the stove which gets very hot.
I think she has singed off some of her fur from this practice, but she is sort of an oddball who cannot be trained.

None of our dogs have ever had trouble with it except laying in front of the fire and being in the way when I try to load the firebox.

Back when the wife and I were still newlyweds, 1980, we got a dog from the pound.  He was a real mix of blood lines.  Heinz 57?  maybe Heinz 85. lol

Well, we brought him home and getting him settled.   I got a fire going to warm up the house.

We didn't think about the dog and wood stove.

The dog was sniffing the stove and all of a sudden licked the door!!!   Sizzling sound of his tongue burning!!  Vet said it would heal on its own.  It did, but was an agonizing few months for that pup.  And he stayed well away from that stove for the rest of his life!