There are a number of errors in the code. The generation of the "months" dictionary is well defined, but keep in mind that the folder names should be in the language of what is defined in the regional settings. In my case it returns in Spanish:
{'JULIO': '007', 'SEPTIEMBRE': '009', 'MARZO': '003', 'JUNIO': '006', 'ABRIL': '004', 'ENERO': '001', 'AGOSTO': '008', 'FEBRERO': '002', 'DICIEMBRE': '012', 'NOVIEMBRE': '011', 'MAYO': '005', 'OCTUBRE': '010'}
The line:
rasterList = arcpy.ListRasters('*Max_Temper.tif', '*Min_Temper.tif')
Will not work, since "arcpy.ListRasters" allows two parameters; the first is the wildcard, the second is the raster type. You are specifying two wildcards. You can either use:
rasterList = arcpy.ListRasters('*_Temper.tif')
... or create two lists and combine them.
The other line where the code will produce an error is:
outRasterName = outCellStatistics, "Mean_Temp_{}.tif".format(monthNumber)
outCellStatistics is a raster object. You will have to use something like (ws_out is your output workspace, and needs to be defined before):
outRasterName = os,.path.join(ws_out, "Mean_Temp_{}.tif".format(monthNumber))