To keep the unit protected from the weather I cover it with a collapsible rubber bucket. By threading each of the two power cords through a handle on the bucket, it keeps the bucket over the transformer even in heavy wind and rain. This could be used with other external surge protectors as well. Also the bucket can be used to get water when needed!
I use something similar for the controller for my bbq's. Usually it works pretty well.
The gotcha here is that the autotransformer may need some ventilation. A lot depends on it's power rating, how much power you are pulling, and how the transformer was designed. Even in normal operation, some transformers can get hot enough to melt a plastic bucket.
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