UnderRail rewards specialization. Guns require Perception; Psi requires Will. You're not going to be able to invest heavily in both because you only have enough stat points to go heavy into one stat. If you're playing on Normal difficulty, you should be fine, though. Still, your metathermics won't be doing amazing damage, or else it will be and your shotgun won't be. May also be tough to scrounge up enough stat points to have a good dose of Constitution, which means as a tank you'll be somewhat weaker than you hope. Additionally, assuming you plan to have something like 12+ in your core combat stats, you're not going to have a lot of room left for INT so you'll need to plan on setting aside a bunch of points for crafting and hacking. Fortunately you're planning on heavy armor so you shouldn't expect to go heavily into Dodge or Evasion, so your skill points won't be spread out too painfully.
It's not a great pairing. Metathermics needs all the points it can get to be in any way impressive. Guns need all the skill points they can get to be in any way impressive. Fortunately, Normal is fairly forgiving, and with your 250+ effective skill come end game, you should be fine.
The build concept is viable for Normal or Hard, and with some significant reloading or heavy use of traps, even DOMINATING. It would be even better if you'd slip 25 points into Psychokinesis so you can pick up Force Field (since you're already a psi character), 35-75* points into Thought Control so you can get enough Neural Overload to handle doppelgangers (which are immune to mundane weapons), and maybe 50-60 points into Thought Control so you can enjoy the very potent psi haste. See, all four psi schools need the same stat, and three of the most powerful feats in the entire game are psi, so if you're going in hard for one, it's difficult not to recommend you pick up at least enough of the others for Force User, Premeditation, *Locus of Control, and maybe Pyromaniac. Those are all really fantastic feats and will be hugely helpful for your build concept. However, that does also make you a quad-school psion, at which point the shotgun is only holding you back.