It depends on what kinds of questions you want to answer. If you want to know if autoclaving is as effective as pasteurization then you have the right design. If you want to know if pasteurization has an effect on fungal growth then you will need an untreated control. You might want a simple control if there is a chance that the media or growing conditions are bad for fungal growth. This can be three petri dishes for each fungus that are untreated and left in the same area. These are not part of the experiment that is analyzed, but are discussed in the results section just to prove that you are able to get good fungal growth and are able to detect that growth with the methods used.
You may have issues with a large number of zeros. Might you get no colony formation at 120 days except in one plate where (for whatever reason) the sterilization procedure was not perfect and one colony forms?