As the yeast ferment, they create heat from the metabolic cycle that can add up to like 10°F to your must. So around 85 degrees? That isn't terrible but it could create off flavors for sure.
did you get your plastic vessel from a brewer's supply website? If not, you need to be aware that there are different types of buckets which should not be used for consumables as they leach from what's stores in them. Potentially dangerous, you can imagine.