When assuming a constant soil heat capacity of 2.1 MJ m-3 °C-1 and an appropriate soil depth, cal_soilHeatFlux_general can be used to derive G for monthly periods.
cal_soilHeatFlux_monthly(T1, T0, Tmonth2 = TRUE)
A vector for soil heat flux [MJ m-2 day-1]
air temperature at time i [degrees Celsius].
air temperature at time i-1 [degrees Celsius].
Is the mean air temperature of next month know?
Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. FAO Irrigation and drainage paper No. 56. Rome: Food and Agriculture Organization of the United Nations, 1998.