Yes, the motor you hear is the coolant pump for the battery, I believe. More moderate temperatures are probably good for the long term life of the battery, but I doubt it makes a big difference. If there is a way to cool/ventilate the garage a little, it might be helpful for extending the battery life, but again, I wouldn't worry about it if it isn't practical.
Yes, the motor/fan sound you hear is for the coolant system. One thing I've found that helps your battery charge better inside a garage is to leave the door or doors open about 4-6 inches to allow for airflow. Using a box fan to circulate the air in the garage also helps.
Not only will this help your battery charge slightly faster, but it can also help reduce battery degradation due to heat.