Quick question

So I started curing my buds in 32 oz mason jars, the hygrometer is reading at 62%. My question is, while storing my jars somewhere will the temp and humidity outside the jar effect the cure?

Outside humidity will have no effect if the jar is sealed. Heat will degrade the THC, as will light. For long term storage, a cool, dark place is best. If you've got room in your freezer, even better!