Effects of encasing bluetooth chip and rechargeable battery in an adhesive encapsulate?
If the Bluetooth antenna is inside the potting compound, it will certainly be detuned. It will quite likely cost you 10 dB of signal, or 3 x shorter range (to a phone... 10x between potted circuits). This applies whether the antenna is a track on the PCB or a bought item.

This effect can be solved by making a version of the board specially tuned for potting. This one won't work properly in air, but will work once potted.

The way you do this is simple: make a potted version that you can still open up to adjust. Coat the board with some release agent - spray 'n cook, light oil, and pot it halfway. Allow it to set. Then coat the surface of the potting, and add more compound until it's fully potted.

Now you have a PCB on which you can easily adjust the antenna and tuning network, but also test in the fully-potted environment.

The same effect happens when you out the circuit in a plastic case, but to a smaller extent, and it's easier to open up to adjust.

Don't worry about it heating up unless the circuit has a fan or heatsinks.
First of all, a small Bluetooth PCB probably lasts a long time on a single battery, so its heat output is tiny.  Secondly, the potting compound will conduct the heat away better* than air will, so it will quite likely run cooler. (* this isn't true if you have heatsinks on chips, then air movement is better).