We show here for the first time that short chain poly( N-isopropylacrylamide) (PNIPAM), one of the most famous thermoresponsive polymers, self-assembles in water to form (i) discrete nanometer-globules and (ii) micrometric sheets with nm-thickness upon addition of the well-known Keggin-type polyoxometalate (POM) H3PW12O40 (PW). The type of self-assembly is controlled by PW concentration: at low PW concentrations, PW adsorbs on PNIPAM chains to form globules consisting of homogeneously distributed PWs in PNIPAM droplets of several nm in size. Upon further addition of PW, a phase transition from globules to micrometric sheets is observed for PNIPAMs above a polymer critical chain length, between 18 and 44 repeating units. The thickness of the sheets is controlled by the PNIPAM chain length, here from 44 to 88 repeating units. The PNIPAM sheets are electrostatically stabilized PWs accumulated on each side of the sheets. The shortest PNIPAM chain with 18 repeating units produces PNIPAM/PW globules with 5-20 nm size but no sheets. The PW/PNIPAM self-assembly arises from a solvent mediated mechanism associated with the partial dehydration of PW and of the PNIPAM, which is related to the general propensity of POMs to adsorb on neutral hydrated surfaces. This effect, known as superchaotropy, is further highlighted by the significant increase in the lower critical solubilization temperature (LCST) of PNIPAM observed upon the addition of PW in the mM range. The influence of the POM nature on the self-assembly of PNIPAM was also investigated by using H4SiW12O40 (SiW) and H3PMo12O40 (PMo), i.e. changing the POM's charge density or polarizability in order to get deeper understanding on the role of electrostatics and polarizability in the PNIPAM self-assembly process. We show here that the superchaotropic behavior of POMs with PNIPAM polymers enables the formation and the shape control of supramolecular organic-inorganic hybrids.