Two suggestions, both fairly simple.
First of all, pets just consume far too many materials, and heating them through the clockworks does barely anything at all. The first suggestion is simple, make the amount of heat needed to level up a sprite less, so players can choose to level them up by either cramming with mats or by playing spiral knights.
The second idea is simply to make it so players can open the forge and feed pets at party buttons. Honestly how many times have you been in a party when someone says "hold up, I'm gonna go to haven to forge/feed pet". And I know I do this a lot. It ruins the flow of dungeoning and makes people have to continually go back and forth after each level just to heat up a weapon.
Thoughts?
Far too many materials? Give them their favourite food and it's 10 per level (5 food, 2x mats each) And that's only at high levels.
From level 0 to 50 1 or 2 5* mats instantly levels them up
"hold up, I'm gonna go to haven to forge/feed pet".
This only happens in boss runs. Kinda funny. You can do regular arcade instead. There are stations on every floor.