Having rewards for the achievements would provide more of an incentive to get them, besides the feeling of accomplishment. It'd give players a goal, really, because there's no such thing as quests or anything in this game... something to aim for, besides getting good equipment or beating the two bosses of the game. For example, 'World of Moorcraft' would give a small sum of crowns, or something. Of course, some achievements don't have to give rewards, and I just used 'World of Moorcraft' as an example because it's the first thing that came to mind. :P
As I write, I was thinking that there should be equipment-related achievements that don't involve crafting directly; that is, defeating 100 monsters with a sword would net you an achievement, or blocking 100 attacks would give you some sort of shield-related achievement. Something that can tie into these kinds of achievements would be general boosts to your character's performance-like increased attacking speed, decreased charge time, more range, higher shield HP... of course, it wouldn't be overkill, breaking the game. It'd substitute for the general idea shared by RPGs-leveling up your character gives better stats, so you can defeat stuff faster and get more EXP, getting to a higher level... repeat, repeat. In that sense, you'd be 'leveling up' that aspect of your character. Heat levels just doesn't feel that fun, mainly because it's equipment-based-it doesn't feel right, for whatever reason. Like your equips make the character, and that's it.
I mainly think achievements should have more of an impact on the game because as of now, Spiral Knights is... fairly monotonous and, sadly, without much variety in levels. After you play for a while, it gets tiring to go through levels, and since there's only two bosses in the game... yeah, there's not much to it. Either the game needs to be larger (more than just three tiers), or there needs to be more special levels-not increased chance of getting them, but more TYPES. Achievements playing a part would help make the game more entertaining in the long run.
I'd suggest some achievements myself, but I don't want to look like an imbecile, because I'm not all that creative. =/
http://www.escapistmagazine.com/videos/view/extra-credits/2758-Achievements