Milky mushroom is Calocybe indica, called dudhiya because the young mushroom is milk white. ICAR-DMR says one milky crop can be taken in almost all the plains of the country, leaving out the hills, wherever temperature stays between 25 and 40 C for some months.
That sentence is the whole species argument. White button fruits at 15 to 17 C air, which on a plain in April means a refrigeration plant. Milky fruits at 30 to 35 C and, in DMR's words, keeps producing even at 30 to 40 C. It matches weather you already have.