I can only speak for my stove, but 1,250*F is NOT AT ALL hot for my VC Winter Warm Large. I regularly get 1700*F temps and beyond that are said to be ok 'for the cat' (according to Condar, the maker of my cat, and probably yours, too) for short periods. I've had 'em, and no harm done. My Condar digital probe cat thermometer even has a scale on it that says operating temps are between 1000*F and 1700*F. These are acceptable CONTINUOUS operating temps suggested by the maker of my (and probably your) cat and my dig cat probe therm. No problems there.
I view 1200*F - 1250*F as an IDEAL cat temp on my stove with the digital cat probe thermometer located on the exhaust side of the cat (hottest side).
Each time I engage my cat, my temps rise well above a 1200*F - 1400*F range. Then 'settle into' that range for a while before eventually dropping off. I refuel at 800*F - 1000*F depending on how much heat I'm needing in a big room, but with me sitting smack dab in front of the stove only about 6 feet away. I can warm the room, or just warm my sitting and viewing area.
I find there is (sometimes) a (somewhat) counter intuitive relation between the flames I see and the cat temps. Lots of flames in the firebox sometimes equals (relatively) lower cat temps. Few flames in the firebox (sometimes) means much higher cat temps. It makes since if you consider that smoldering wood produces a lot of smoke that is then burned by the cat. The more smoke that gets burned by primary combustion, the less there is left over for the cat. It's interesting. That's why I like the digital probe thermometer. It always lets me know what is going on with the otherwise mysterious cat temps. I am astounded at the high cat temps at times when there appears to be NO fire burning at all. That's one thing nice about a cat. You can maintain a really slow burn if you want to, and not be polluting like crazy as long as your cat is lit off and at operating temps (1000 - 1700). This can save wood IMO regardless of all the conflicting opinions. Slower burn equals slower wood consumption. Of course, if you aren't sitting right in front of the stove, need to heat up a big room, etc., then you may not desire to burn as slow as Mo.