Hi,
You can perform your requirement in steps. For example, you can sort the temperature first then find the maximum one depending on the month. You can take help from the below-given example.
require(data.table)
DT=as.data.table(airquality)
DT[,.SD[which.max(Temp)],by=Month]
Month Ozone Solar.R Wind Temp Day
[1,] 5 45 252 14.9 81 29
[2,] 6 NA 259 10.9 93 11
[3,] 7 97 267 6.3 92 8
[4,] 8 76 203 9.7 97 28
[5,] 9 73 183 2.8 93 3