Yeah, I may be new to the forum but not to batteries.
Since you didn't say a particular voltage when asked when you recharge, I say recycle those batteries (or return them)... buy new ones from a reputable source... buy a multimeter... learn to use the meter, but don't trust it to measure your coil resistance unless it's just a part of a 4 wire set up and you know the error tolerances. Speaking of, what were you using to check your resistance?
If you are 0.33 Ohms... you are likely using somewhere between 30-50+ watts(VA) or between 9-13 amps which is where knowing your voltage under load can be useful.
The fact the button was getting warm is something I have seen people talk about when drawing too many amps from a battery (which heats up) and since conductivity relates (not exactly equal to though) both electricity and heat, you can feel it on the nearby button.
Maybe once you bring out the meter, you can check what current you are drawing with that complete set up.