HOMER does not synthesize hourly temperatures from monthly averages the way it does with solar radiation and wind speed data.  It would be great if it did, but we haven't found an acceptable synthesis algorithm yet.  So, if you enter monthly temperature values, HOMER just assumes that the temperature remains constant throughout each month. Therefore, if you require precision in the ambient temperature data, you will have to find hourly data somewhere, and import that data file into HOMER.

If you are in the US, I recommend the TMY3 data set; it contains 'typical meteorological year' data for over 1000 locations in the US. It's a great data set for the kind of modeling we do with HOMER. You can find it with a Google search on 'TMY3'.