Hotter and drier years appear to reduce growth of mite populations,  
principally by reducing mite reproduction:

https://www.ars.usda.gov/SP2UserFiles/Place/64133000/PDFFiles/401-500/412-Harris--Variable%20Population%20Growth.pdf

Exactly how does this happen?  Not very clear.  Colonies seem to  
regulate both temperature and humidity fairly well where brood is  
being reared.  We did not publish these negative results but Diana  
Sammataro placed temperature and humidity recorders in cutout sections  
in the middle of brood areas in colonies in Arizona, and I did the  
same in Louisiana.  Predictably outside desert temps inside empty  
hives were higher, humidities lower than in the humid south.   
Surprisingly temperatures and humidities inside the brood nest of  
colonies in both localities were essentially the same.

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