if 15 V is used to charge a 3.5 V battery, will the battery explode?
Yes, I am pretty sure you could find a way to use 15V to make 3.5V Lithium battery explode.
Assuming you don't actually want to do that, you'd need to know the specific Lithium chemistry. Each type of Lithium chemistry requires a different charge profile. Once you find out the specific chemistry (and even if it is rechargeable or not), do a google search on charging that particular type of battery. As jackrae says, they can be real fussy. Some types have built in protection circuitry and if you abuse them they will brick themselves to avoid that explosion you mentioned. At that point you can just go out and buy a new battery along with the proper charger.