Will this lithium ion battery cause too much heat and fry components?
The fact that a battery - or any power source - is capable of supplying a certain amount of current does not imply that the circuit in question will draw that much current.

Your question puts the cart before the horse. You need to determine how much current your project will draw first. Consider as well not only the average or steady-state current draw, but any surge current (particularly at startup). Once you know that, then you can go back and determine whether a particular power source will work.