Hello Barone, and welcome to Firestryker.The best padding to use for the best results, both in comfort in wearing, and in mimicing the original garments would be to use what our forfathers originaly did.
This usually equates to linen. A garment like what you post might also have an additional stuffing of tow - the by-product of flax. Popular in Italy also was raw cotton - several helmet liners exist which are stuffed with raw cotton.
Natural textiles breathe, while synthetics do not, as you have noted in your experiment. 
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Bob R.