'non-perspiring' is formed from the prefix 'non-' (a Modern English negative prefix ultimately from Latin via Old French) and the verb 'perspire', specifically the Latin word 'perspirare', where 'per-' meant 'through' and 'spirare' meant 'to breathe'.

'perspirare' entered English through Late Latin and Old/Middle French influences, appearing in Middle English as forms like 'perspiren' and eventually becoming modern English 'perspire'; the negative prefix 'non-' was attached in Modern English to create 'non-perspiring'.

Originally 'perspirare' literally meant 'to breathe through', but over time 'perspire' developed the specific sense 'to emit moisture through the skin (to sweat)'; consequently 'non-perspiring' now means 'not sweating'.