Here are definitions/translations from various dictionaries.
Oxford Hindi-English dictionary:
तासीर tāsīr [A. tās̤īr], f. effect; action, manner of operation (as of a medicine).
Platts’ Urdu, Classical Hindi, and English dictionary:
A تاثير tās̤īr [inf. n. ii of اثر], s.f. The making an impression; impression, effect; operation; penetration (see as̤ar): — tās̤īr karnā (-meṅ, or par), To make an impression (on), take effect (on), to influence: — tās̤īr kam karnā (-kī), To diminish the effect or the efficacy (of): — tās̤īrāt, s.f. pl. (of tās̤īr, q.v.).
It is not possible to translate it very well in English, as the concept does not exist in English-speaking cultures. You can go for "property" as your best option, in my opinion. Another very good option would be to leave it untranslated and explain the meaning in a footnote or glossary.
I'm afraid I don't know the answer to your question, but the health system of ancient times, which postulated the four humours, did classify foods according to hot, dry, wet and cold. I'm sure there must have been similar vocabulary to what you're looking for in older English, and perhaps enquiring somewhere where that type of information would be known could help turn up the word you're looking for.