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Heating peroxide will only turn it into water and oxygen so that it is no longer useful.
Here is a method for removing pet urine from carpet.
1. First remove any wet urine using the "stomp on plain white paper towel" method. This also works on old stains.
2. Mix 1/2 cup white vinegar with 1/2 cup water and saturate the area. Work it into the deepest fibers with your fingers (you will want to wear rubber gloves) or a brush. Repeat the paper towel stomp. If you have a vaccum extractor, that really saves a lot of time (and apper towels). Figure on a roll of paper towels for the entire procedure unless you have a really tiny spot. It is the white vinegar that breaks down the ammonia in the urine (either old or new urine).
3. When the area is dry, or nearly so, (a fan directed at the area speeds things along), sprinkle a big handful of baking soda on the area to cover it.
4. Now comes the hydrogen peroxide. Mix 1/2 cup 3% hydrogen peroxide with 1 teaspoon dishwashing liquid (Joy, Ivory, Palmolive, Dawn, etc.. NOT Cascade, Finish or other automatic dishwasher product.). Slowly pour the peroxide-detergent mixture over the baking soda. It will foam. Again use your fingers or a brush to work it into the carpet fibers.
5. Allow to dry (again a fan helps).
6. When completely dry, vacuum up the baking soda. You can use a dry brush to loosen any baking soda remaining deep within the pile.
7. That should eliminate the odor completely. If desired, you can clean again with plain water to remove any residual dishwashing detergent, but it usually isn't necessary.
This also works for cat urine and poop.
All the best,
Sorry I thought you were asking about carpet. Wooden floors generally should not have liquid put upon them at all. As for upholstery, some are color-fast and others aren't. I would try the recipe on an underside of a cushion before attempting to treat an area that will be seen, just to see how the fabric reacts.
For wooden floors, I would consult a professional floor refinisher. Anything under the varnish is probably going to require refinishing the entire floor since getting the colors to blend after treatment would be a task beyond what most homeowners are willing to undertake. When the varnish is off they can treat for urine and then revarnish after the spots are dry. If you still have the dog and s/he is prone to accidents, you could ask about a finishing product that is more durable than usual to protect your floor from future mishaps.