That's what you expect, but the Aztecs went heavily into
ichcahuipilli, which was a quilted cotton armour and could be regarded as the equivalent of a gambeson in terms of protective quality.
If anything, they would be less likely to wear bronze armour due to the outermost non-breathing metal layer preventing heat loss to the environment (some conquistadors were reported as preferring to use the Aztec's armour rather than their own cuirass as the loss in protection was well worth the additional comfort).
Spoiler: Aztec armour in the Codex Mendoza, 16th Century
Show
I'd also say that it depends heavily on acclimatization - if you're used to living in a jungle environment, then wearing protective clothing wouldn't be as restrictive.