I found this which shows the mean humidity levels in my region:
http://www.bom.gov.au/climate/averages/tables/cw_023034.shtmI did some measurements today. It's been between 41% and 53%, from morning to dusk. Inside my chest freezer, the humidity level was in the low 30s. Having the heater on, and off didn't seem to change much. I notice that, there already is a slight gap for moisture to escape, since the electrical cable for the oil heater keeps the lid open very slightly.