The 2-fold thermoresponsive diblock copolymer PSPP498-b-PNIPMAM(144), which consists of a zwitterionic polysulfbbetaine (PSPP) block and a nonionic poly(N-isopropylmethacrylamide) (PNIPMAM) block, is, prepared by consecutive RAFT polymerizations. It combines the upper and lower critical solution temperature (UCST and LCST) behaviors, respectively, of the constitutive homopolymers' in aqueous solution. We investigate the temperature-dependent phase behavior and the self-assembled structures of the block copolymer in D2O by turbidimetry and by small-angle neutron scattering (SANS) in salt-free solution and in the presence of small amounts of NaCl and NaBr. For comparison, solutions of PNIPMAM homopolymer in D2O are studied as well. Turbidimetry indicates thermally induced "schizophrenic" aggregation behavior for PSPP498-b-PNIPMAM(144). SANS reveals that conventional star-like core shell micellar structures are formed above the LCST transition, whereas below the UCST-transition, structure formation is much less pronounced. This is attributed to the different types of interactions, namely hydrophobic and ionic ones, dominating in the different regimes. Despite the increased polarity contrast between the zwitterionic and the nonionic blocks, and the much wider separation of the UCST- and LCST-based cloud points, CPUCST and CPLCST, the structural features of the new PSPP498-b-PNIPMANI(144) resemble the ones found previously for the also 2-fold thermoresponsive. analogue PSPP(432)b-PNIPAM(200), for which both phase transition temperatures nearly coincide. Remarkably, the addition of small amounts of NaBr or NaCl to the solution of PSPP498-b-PNIPMAM(144) causes a significant increase of CPucsT, as well as minor but notable changes in the self assembled structures, but no gross alterations of the phase behavior.