You don't have to remove the battery completely, but you must be sure to break the contact. If you have the pushback ring installed then all you have to do is stop pressing on the battery.
Having the battery get too hot can potentially damage the battery if it happens too often. The "damage", if it occurs, will show up in a reduction in the number possible charge cycles. Perhaps after a bad overheating (fully charged to nothing in one 5 minute stroke) a battery instead of lasting 500 recharges, it will only take 400. Magic-Flight says "60 seconds" because they know and are certain that that is "soon enough" to be sure to have no problems. Performance in a battery decreases in proportion to its abuse.
You can probably get away with longer than 60 seconds if you are paying attention by checking the battery warmth, but that isn't recommended. If you use the same battery without even a moments break for more than 2 solid minutes, it can also get too hot to touch comfortably. One answer is to use two batteries in alternation, if you want continuous Box heating (about 10 minutes worth).
Also, to put this into perspective, note that these concerns apply to all NiMH type batteries, not just the stock ones. Energy is energy -- all of it carries some risk, regardless of form. For example, butane lighters can explode if thrown in a fire. Similar problems apply to Li batteries. To be safe, Magic-Flight ships battery cases with all outgoing stock. Respect the batteries by always putting them in their case when not in active use. That will ensure that they last a long time and never cause any trouble.