It seems that both the heroes of pre-bronze age collapse and the Aryans of the Vedas share many cultural characteristics, having adventures, conquering things, doing everything you would expect from an expansive group like the hypothesized PIE speakers. I'm wondering if there is an etymological connection between the terms. I've only found that hero has a debatable etymology, and Aryan was a self designation for the indo-Iranian branch of PIE speakers, and has debatable relations to self-designations for an elevated social status in other branches. Please please don't turn this into a weird Nazi thing.
The origin of "aryan" is well attested: Sanskrit arya- "comrade, fellow," thence Old Persian ariya- as a self-identifier. It comes to Greek (and then Latin) as an ethno-topographic word, Aria or Areia, always in reference to the area and peoples of eastern Persia. It certainly had nothing to do with white people. That association comes millennia later, as the word was continually reinvented.
Hero is not as straightforward. The earliest we can get is Greek ἥρως; [m.] 'lord, hero.' It used to be assumed to come from a root with a digamma, ἡρωϝ-, but the discovery of Mycenaean ti-ri-se-ro-e now points to the PIE root *ser- "protector," or to a pre-Greek (ie non-PIE) root (per Beekes).
Either way, it is very very unlikely that the two are related, and the Myc attestation is the nail in that coffin. The words are just shaped differently and seem to come from very different inputs.