  We have analyzed the thermodynamics of slowly rotating magnetized Kerr
black-hole, with typical spin parameter $a\le 0.1$ (nearly static) in the
background of non-linear electrodynamics. In particular we have studied the
Bekenstein-Hawking entropy, Hawking temperature, angular momentum, specific
heats and identified regions of parameters for possible phase-transitions. It
turns out that once the stability lost the black-hole never come back to its
original stable position.
