  We investigate deformations of the Kerr-(A)dS near horizon geometry and
derive partial infinitesimal rigidity results for it. The proof comprises two
parts. First, we follow the analysis of Jezierski and Kami\'nski [Gen Rel Grav
45 (2013) 987--1004] to eliminate all but a finite number of Fourier modes of
linear perturbations. In the second part, we give an argument using analyticity
to prove that there are no odd Fourier modes.
