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Can I use a normal battery for mobile (3.7v) in the jbl micro wireless? The original battery has a transistor (or whatever) together. If so, what would change in the functionalities?

Sadly you’ll need to get the proper Lithium Ion battery for your device, you can’t use just any battery. The device which you identified on the battery is a thermal sensor to monitor the temp when the battery is being charged so the battery is not over charged.