As mentioned by others, but encourage to repost in the original post, there is definitely issue with the new Death punches, the Bunker Shell and Magma Blast.
They simply do too much in a single action, and multiplayer is an environment where every action counts. They do crazy high hp damage, drain resistance, drain total reserve, and inflict huge heat/energy damage and they do it all in a single action. It takes 2 shots from any other weapon to do what this weapon does in 1 action.
Not only this, the firing range is extremely generous. I believe it's 2-6, though it could be 2-4. The old death punch, you could hide under the gun range of it by fighting in close with melee and flamers. This new one you can't duck under, one stomp puts you into range.
I would suggest:
Keep the outrageous high damage, it's nice to have a pure high damage heat/energy weapon type.
1. Dramatically reduce the heat damage/energy damage inflicted by these weapons. They don't need to and shouldn't ever do 700+ damage (bunker shell vs energy depleted target).
2. However much heat/energy damage they inflict, cut it in half so it's no more than 100.
3. Change the range of the weapon so it's clunky to use. A lot of old weapons were like this, too many new weapons are too easy to use. Old tactics positioning to avoid certain shots was important. If the Bunker Shell or Magma Blast only had 1 range they could fire at, say range 3, it would offset their ability to do so much in a single action.
For example: if it can only fire at exactly range 3...
You spend a move action to line up that perfect range 3 shot. Now you're spending 2 actions to deal that outrageous damage/heat/energy, which is in line with what normally takes weapons to do.
Your enemy knows to stay out of this specific range, and if they set themselves up for a double hit, a 2 with a push into a 3 range Bunker Shell/Magma Blast, well it's their own fault, they could have used a move action to prevent this from happening.
End result, move actions and positioning become more important and you can never combo 2 Bunker Shell/Magma Blast together in a single 2 action turn.
As for the new 3 use mythic flamethrowers, I don't know but these things are just silly. Doing 300 energy damage in a single turn is just unbeatable. If they go first, and fire that, they're gonna win. Even if you have all weapons with no energy dependence, you're too far behind and are going to take too much extra damage from being energy drained to fight back.
I would reduce their energy/heat damage to half of what it is. 300 energy from a max mythic blue flamer reduced to 150, which is still higher than another other single weapon in the game. Although maybe not that Blue Valiant Sniper or whatever it is, but as mentioned by others, that also needs adjustment.
At least this way, you have to get hit by 2 of these flamers to suffer catastrophic 300 energy lost. And considering they have 3 uses over the old mythic 2 use flamers, I'm not even sure they should get a buff to compensate. Just straight nerf.
If a straight nerf is too unfair, give them more armor breaking power. Though I hesitate to say that without knowing exactly what the stats are of these flamers, they could already have crazy high armor breaking/energy total reduction/energy regen reduction built into them as well.