I can confirm the pet appetite does increase faster with heat amps.

Also, the current application of heat amps actually allows you to heat your weapon normally while also heating your pet up as well, so you can in essence still multitask the same way you could before. The new Forge mechanics help dissuade people from constantly farming FSC for as much heat as possible and to actually experience the Clockworks again - this is implied by the fact that boss stratums only have one loadout station in which you can feed your pet, forge your weapons, etc., whereas non-boss stratums have a loadout station to do that at every depth. They wouldn't add that sort of utility to the loadout station unless it was their longterm goal, and the fact that they neglected to change boss stratums to include additional loadout areas also helps substantiate that notion.

So no, the heat amp's working as intended, even if unintended side-effect is for you to go into the Clockworks and forge weapons at each loadout station.

I think I can see what your're talking about. Basically you're referring to how, in the past, gear could receive multiple levelups on a floor, easily fixing up multiple low-grade equipment in about 2-3 floors for example. I remember those days, and it made heat amps very desirable.

Unfortunately, the system is different now, and they're still making adjustments here and there. At this point in time though, I don't think they can think up a good solution to deal with the problem, because the new forge system (and thus the bottleneck you're experiencing) is part of the overhaul they made so that you wouldn't have to be restricted by mist energy in the first place and they're still adjusting a lot of the new changes. Personally I prefer being able to roam the clockworks 24/7 without an elevator pass or paying lots of real money for CE, so I'll take this over what we had before, personally.

However, there IS a good way to prove that heat amps are useless: Don't buy them. Eventually OOO will figure out the hard way that no one is buying them from the Supply Depot or Starter/Battle Packs, just like how they lowered the droprate of Sparks of Life once they realized no one was buying those from the Supply Depot either. I don't think I'll bother buying them because I noticed quite early that they're only really helping pets and equipment grinding on their lv5-9s, and I'm quite comfortable with the pacing I have with my pet so far without paying buttloads of crowns for a minute advantage.

Ah, I think I have something of an idea. Two actually:

#1: What if we made a Forging Pass, similar to the Elevator Pass, where instead the game will automatically forge equipment once they gain max heat, allowing them to accumulate the rest of the heat they gain on a floor? The Max Fire Crystals option should always be picked, and the auto-bypass will not work if you don't have that many fire crystals. Priority to auto-levelups would be given by a user-selected list, or could even only work for one slot that you could freely choose between while at an Arsenal Station. Of course, as mentioned above, the Pass would not work during boss stratum segments, unless OOO didn't intend for that part to happen. Intended as the lazy solution.

#2: Instead of automatically applying heat to equipment as the game has done since its inception, how about we instead have a temporary Heat currency, quite similar to Mist Energy, that could only be held until moving past the wall after an Arsenal Station on the next floor. The "Mist Heat" would decrease based on how much you tempered a particular equipment from one level to the next. That way you could control what levels up and for how much. Intended as an involved solution.

I'm suggesting these in this manner because Spiral Knights already has parts of these ideas implemented in the game design, even if the application of those concepts would have to be reprogrammed to suit the ideas.

re-stating idea again.
every [instert amount here] if heat would rise the crafting success rate of 1%. rewards would not be affected. maybe there should be a cap on the first, but like 75%. so the heat in excess would go into something useful and we can keep the forge.

Heat amps should also increase the drop rate of fire crystals.

I LOVE reading this stuff, its super funny, I say they just add Arsenal stations to start start of most areas, excluding SL's and Boss floors =P

That'd solve the forge, and feeding problem then you can spam away for crystals =P keep up the ideas everything :D