There's a few things going on here. By using the pulsing method, you're essentially shorting out the coil, your pulses should go very fast and ideally if properly insulated, the
coils should get warm from both ends at the same time. Otherwise, you'll see it start at positive and work it's way towards the negative.
It's best if you use this method only if you're very experienced and you know what your end ohms are going to be based solely on your wire wraps and how tight your
coils are. Anything else and you're risking running a very low ohm setup that may be too much for your batteries. A MM will not help here, because until the coil is oxidized it's going to be shorted.
That all being said; because you're running a shorted setup and slowly spreading through pulsing the oxidation of the coil and mesh at the same time, yes your battery will run warm, which will result in your button getting warm. If it's getting to hot to touch; i'd recommend letting your battery cool down for a few minutes in a well ventilated area (try a fan) Continuing while hot is just asking for a thermal runaway discharge and subsequent venting.
Here's a good tutorial on the topic:
A PBusardo Review - The AGA-T(s) - Part 2 - Assembly & Building Tutorial - YouTube
Hope this helps, and vape safe man!