Make the stove a permanent boundary, not a part-time warning
An AGA or wood stove that stays hot from morning to night is different from a fire lit for an evening. Your dog will cross the kitchen dozens of times a day, often half asleep, chasing a smell, or following you with a toy, and she cannot learn that the surface is sometimes safe and sometimes not. Set one simple rule from the first cold day: the stove and the hearth around it are never her space. A fixed guard that she cannot push aside, jump, or wriggle under does that teaching for you, even when nobody is watching. Leave enough space between guard and stove for the heat the maker expects, and check that paws and a wagging tail cannot reach through when she turns in a tight kitchen.
Give her a better warm place to choose
Most dogs drift toward a stove because it is the warmest, most social corner of the house, not because they love danger. Beat it with a genuinely appealing alternative: a thick bed in a draught-free spot where she can still see the table and the door, with a blanket that smells of the household. Feed puzzle toys and long-lasting chews on that bed, praise her for settling there, and greet her there when you come in. If the kitchen is her usual sleeping place, move the night bed the same distance away as the daytime one, so sleepy wandering at night does not take her past hot metal in the dark.
Manage the risky moments around the stove
Burns in this setup rarely happen during calm hours. They happen when the stove door is open for loading, when ash is carried out, when wet mittens and boots crowd the hearth, or when a pan is carried across a dog lying in the way. Put your dog behind a door or gate for the few minutes of loading and ash removal, every time, without exception. Keep kindling, logs and the ash bucket outside her route between bed, water bowl and garden door, and never dry her towel or hang her lead on the guard itself. Teach a solid settle on her bed before the busy cooking hour, and reward it there, so the moment the kitchen gets crowded her job is already clear.
Watch for heat stress as well as burns
A dog who loves the warm corner can also overheat quietly, especially a thick-coated, older or flat-faced dog sleeping close to constant heat. Panting at rest, restlessness, seeking cold tiles, or drinking far more than usual are signs to move the bed further away and cool the room for her, not signs to let her decide. Check paw pads and the bare skin of the belly and ears after any yelp or sudden jump near the hearth, and if she has touched hot metal, has blistered or pale skin, or keeps licking one spot, contact your vet the same day rather than waiting to see how it looks tomorrow. Her profile access can be given to relatives you select in KinsLe Family Sharing, so family who cook in that kitchen have already seen the dog who must never settle beside the stove.