  We study the near horizon 2d gravity theory which captures the near extremal
thermodynamics of Kerr black holes where a linear combination of excess angular
momentum $\delta J $ and excess mass $\delta M$ is held fixed. These correspond
to processes where both the mass and the angular momenta of extremal Kerr black
holes are perturbed leaving them near extremal. For the Kerr $AdS_4$ we hold
$\delta J-\mathcal{L}\,\delta M=0 $ while for Myers-Perry(MP) type Kerr black
hole in $AdS_5$ we hold $\delta
J_{\varphi_{1,2}}\hspace{-0.2cm}-\mathcal{L}_{\varphi_{1,2}}\,\delta M=0$. We
show that in near horizon, the 2d Jackiw-Teitelboim theory is able to capture
the thermodynamics of the higher dimensional black holes at small near extremal
temperatures $T_H$. We show this by generalizing the near horizon limits found
in literature by parameters $\mathcal{L}$ and $\mathcal{L}_{\varphi_{1,2}}$ for
the two geometries. The resulting JT theory captures the near extremal
thermodynamics of such geometries provided we identify the temperature
$T^{(2)}_H$ of the near horizon $AdS_2$ geometry to be
$T^{(2)}_H=T_H/(1-\mu\,\mathcal{L})$ for 4d Kerr and
$T^{(2)}_H=T_H/(1-\mu\,(\mathcal{L}_{\varphi_1}+\mathcal{L}_{\varphi_2}))$ for
5d Kerr where $\mu$ is their chemical potential, with $\mu\,\mathcal{L}<1$ and
$\mu\,(\mathcal{L}_{\varphi_1}+\mathcal{L}_{\varphi_2})<1$ respectively. We
also argue that such a theory embeds itself non-trivially in the higher
dimensional theory dual to the Kerr geometries.
