If, by "tech shirt," you mean something that will wick moisture away from your skin, so it evaporates, rather than holds it: Under Armor's products beat everybody else's, hands-down. I've tried others, but UA's work best, IME.
UA does make long-sleeve versions.
Costco has tees, made of a similar, but thinner, material that work well as an undershirt, at a fraction of the cost. Later in the season they might be carrying the long-sleeve version, again. The stuff is called "32° Cool."
A week ago, when I was giving my new build its trial run, I was wearing one of those 32° Cool shirts. Over that I wore a short-sleeve Field & Stream collared, tail-less shirt, designed to be worn un-tucked, as a cover garment. (Much less obvious than a "shoot me first" vest.) It is also made of a tech fabric. My head sweated under my ball cap, but my upper body stayed dry and comfortable.
You can buy hats made of similar materials. They work, trust me.