A lot of balers have moisture meter's on them to tell you the moisture content of the hay. You can also check the moisture content of the hay before baling/rolling with a moisture meter.
I would add, if you have any suspicion that the moisture content is too high after it is baled, do not put those bales in a barn. Every year a lot of barns burn because of this.
Ended up getting a long soil thermometer and taking the bales temps, from what it says online anything below 130 degrees should be fine to put in the barn. Had some above that so just letting them cure.
