Hello, devs!
Right now, the difficulty increase that comes with going into Tier 3 does not match the amount of heat that is obtained in that same Tier. A full run of Tier 2 is both less expensive and more productive right now in terms of heat gain than Tier 3 (or, at very worse, identical).
This was tested by having two separate Sealed Swords and going into two roughly similar patches of stratums in Tier 2 and Tier 3, solo. From the first stratum to the Terminal, the Sealed Sword in Tier 2 went up 3.3-3.6 heat levels, while the Tier 3 one was somewhere in the 2.5-2.8 range. That's... ridiculous? Absurd?
You can actually sort of see the difference as well, because a monster in T2 seems to drop a few more heat orbs than one in T3. The only levels in T3 that seem to produce any substantial amount of heat are the Firestorm Citadel, and even then they're not as good as the Jelly King.
It does seem to me that the heat/crowns are less lucrative at the start of a tier than the end of it, which is fine, but as you said, the latter half or tier 1 / tier 2 shouldn't be less profitable than the first half of tier 2 / tier 3, right?
Maybe its on purpose to encourage the players to not abandon those tiers once they've passed them? Not sure really, but it does bother me when I do a Tier 1 to midway through Tier 2 run, and the profits aren't as good for those last few floors as they were before Moorcraft Manor.