  We investigated the complexation of thermoresponsive anionic
poly(N-isopropylacrylamide) (PNiPAM) microgels and cationic
$\epsilon$-polylysine ($\epsilon$-PLL) chains. By combining electrophoresis,
light scattering, transmission electron microscopy (TEM) and dielectric
spectroscopy (DS) we studied the adsorption of $\epsilon$-PLL onto the microgel
networks and its effect on the stability of the suspensions. We show that the
volume phase transition (VPT) of the microgels triggers a large polyion
adsorption. Two interesting phenomena with unique features occur: a
temperature-dependent microgel overcharging and a complex reentrant
condensation. The latter may occur at fixed polyion concentration, when
temperature is raised above the VPT of microgels, or by increasing the number
density of polycations at fixed temperature. TEM and DS measurements
unambiguously show that short PLL chains adsorb onto microgels and act as
electrostatic glue above the VPT. By performing thermal cycles, we further show
that polyion-induced clustering is a quasi-reversible process: within the time
of our experiments large clusters form above the VPT and partially re-dissolve
as the mixtures are cooled down. Finally we give a proof that the observed
phenomenology is purely electrostatic in nature: an increase of the ionic
strength gives rise to the polyion desorption from the microgel outer shell.
