Question about 3.7 LiPo Battery

I want to use a LiPo battery for my wearable device but I am wondering if it might potentially warm up when in use, causing a lot of uncomfort for the person wearing the device? It will not draw more then 40mA

40mA would not be noticeable. That's like the current for 4 LEDs at 1/2 rated power. At peak voltage, 4.2V, power being drawn, and dissipated by the circuit, is 4.2V x .04A = 168mW.

no pb with 40mA, but.... ...make sure you avoid any risk of a short between + and - , because it would be really dangerous ! (even if this one has an over current, protection, it could get very hot if shorted)