Hamon method is for ET calculation in daily scale, but I think you can consider Average Ta and D values for a month and go ahead. Or Go for Thornthwaite, Blaney–Criddle.
this kind of empirical formula with few parameters are always risky because their physics is weak. From that point of view, the Penman-Monteith equation is best equipped. Yes, you need more parameters but it brings you much closer to actual values. You could calibrate it for the present and then extrapolate that into the future.