WALL OF TEXT WARNING!

I would think at this point more people would benefit from fire crystal drop amplifiers rather than heat amplifiers (at least for F2P people)

I'm not sure how useful heat amplifiers are for those without fire crystals, and of course, the very thing I'm referring to is the lack of radiants.

For 50 radiants, the cost I believe is 700 energy. Compare that to the cost of 3 eternal orbs, which is 800 energy. It would seem that forging has a higher value than crafting 5* items now. 50 radiants will suffice for those lower levels, but there are varying factors, such as how many crystals you want to use for improving success rate and the chance of a forge box.

My point is that for someone who doesn't play much, especially for crowns or radiants (OCH/vana/shadow), getting radiants are quite time consuming (and luck will play in terms of how much you get), and therefore getting a heat amplifier won't be as beneficial. Emphasis on "as". There are some who can still use heat amplifiers.

Now about the mechanics for this fire crystal amplifier, there are few ways this can work:
1) increase chance of crystals per box
2) increase number of crystals per drop
3) lower the minimum depth for chance of getting a higher-star crystal
4) few other ways you might be able to think of.

Of course, some may think this may be unbalanced or will unbalance the economy, but if you think about it, 700 energy for 50 radiants. The amount of radiants you get per appropriate depth may vary, about none to perhaps 30? (for me, one of out many OCH elite runs had all boxes full of radiants, I'm not sure if I was dreaming but that's aside from the point).

The range of radiants for crafting according to this table: http://wiki.spiralknights.com/Heat#Fire_Crystals_Requirements
is about 151 (40->20%) to 453 (100%). That means for those with energy, that would cost about 2100 to max one 5-star, and the success isn't guaranteed. For 100% success, that requires 6300 energy.

CALCULATIONS (SKIP IF YOU WANT TO)

Vana is a popular source for crowns, which gives about 8-10k per run. Energy prices range from 7k to 10k crowns, so 100% forging, that's 440k to 630k. For the minimum forge, that's about 150k to 210k. But of course, we're not counting the radiants we get.

I'll work with 630k so we know the maximum number of runs we need. I'll be working with 8k crowns for the minimal earnings. That's about 80 runs for maxing one 5-star equipment. Now taking into consideration we get 3 radiants per run, that's 240 radiants. Little more than half required to max through 100% forging.

Maxing through radiant runs (3 per run):
453 radiants = 151 runs.
Maxing through crowns (8k per run):
453 radiants = 9 x 700 E = 6.3k E = 630k (assume 10k per 100 E) = 80 runs

160 runs would give you enough to max 3 5-stars with both purchasing and crown farming.
So minimally, about 55 runs would be enough for 1 5-star equip.

Least required, assume 10k per vana and 7k for E:
453 radiants = 151 runs
Maxing through crowns:
453 radiants = 9 x 700 E = 6.3k E = 441k (assume 7k per 100E) =44 runs

160 runs would give you enough to max 5 5-stars.
So maximally, about 32 runs would be enough for 1 5-star equip.

Note: These numbers may not mean anything to those who have lots of time available. These calculations are not also 100% accurate as rounding has taken place.

3 vanas per day may range from 10-20 days per 5-star with both purchasing and farming.

But of course, all SK players may want to spend their crowns on something else, not just radiants.
So if a fire crystal drop rate amplifier would be added, I'd think the cost should be generally lower than how much you make in those 151 runs, but not too low or else SK may not benefit from energy prices. Since 6300 E is required for just one 5-star 100% forges, I'd think somewhere between 4500 and 6000 would be good. (regardless of how expensive it is, I believe SOME profit should be made. Not too much though. That may unsettle the economy) But then again, depending on how effective the rate amplifier is, the price is subject to change. For example, a really effective one would require the price to be higher.

Things to consider:
Price of amplifier
Duration of amplifier