Pity I did not see the new posts earlier. primem0ver, I might have a solution for your problem:
A scientist named Baart Geerts has developed calculations to estimate the climate of a location empirically based on its geography. I believe that these calculations could be used to give the results you are looking for, in a fairly accurate way.
Obviously, Geerts' calculations are based on empirical data from Earth. So, if we are trying to calculate the climate for a planet with a very different continental layout from Earth (a pangaea, or an archipelago world consisting of nothing but small islands), the results will be somewhat off (but probably still useable). If, however, the planet has a similar continental layout to Earth (a few big continents and a few big oceans), the results should be quite accurate.
Sources:
Geography and climate (the very simple version, for students)
Empirical estimation of the annual range of monthly-mean temperatures (more advanced)
Here is how it goes:
From the latitude L (in degrees) of a location and the altitude h (in meters), you calculate the mean annual temperature Ta (in degrees celsius):
Ta = 27 - 0.0077 L² - 0.005 h
Secondly, with the latitude L (in degrees) and the distance d from the upwind coast (in kilometers), you calculate the annual range of temperatures Ra (in degrees kelvin):
Ra = 0.12 L d^0.2
According to Geerts, the mean absolute error when comparing the calculated estimates and the real measurements on a large sample of weather stations around the world is 2.2 degrees K for the mean annual temperature, and 2.6 degrees K for the annual range. Not too bad!
Now, from Ta and Ra, you can calculate the mean temperature of the warmest and coldest month, Twm and Tcm:
Twm = Ta + Ra / 2
Tcm = Ta - Ra / 2
From here, you can extrapolate the mean temperature of all the other months by using a bell curve.
For calculating Ra, the direction of the upwind coast depends on the general latitude and season:
Tropics (0° to 30°): east
Subtropics (30° to 40°): east in summer, west in winter
Temperate zone (40° to 60°): west
Subartic (60° to 70°): west in summer, east in winter
Artic (70° to 90°): east
If the prevailing winds vary by season (as in the subtropics or the subpolar zone), you calculate Ra two times using the equation above, once with d from the west coast and once with d from the east coast, and use the average of the two as your final Ra.
Prevailing winds can also change seasonally if there is a monsoon. We will have to enable the program to recognise particularly large continents (should not be too difficult), and simulate the monsoon over these large continents based on that.
This is the simplest set of such equations. You can refine them by factoring in distance from a north or south coast, an upwind mountain barrier, inland seas and so on and so forth. But let's start with the above, and see how it goes.