A diblock copolymer of styrene and butyl methacrylate with narrow molecular weight distribution [P(S-b-BMA)] containing 1200 monomeric units of S and 1250 of BMA was studied in 2-propanol [2-POH], which is a nonsolvent for the S blocks and a theta solvent (UCST) for the BMA blocks. The phase diagram of the present system is almost indistinguishable from that of 2-POH/PBMA if the molecular weight of the homopolymer is identical with that of the BMA block. The comparison of the intrinsic viscosities [eta] of P(S-b-BMA) and PBMA in 2-POH and of their variation with temperature demonstrates that [eta](P(S-b-BMA)) reflects the presence of micelles rather than unimers. The theological behavior of moderately concentrated solutions can be understood in terms of an overlap concentration c(*) defined as [eta](P(S-b-BMA))(-1). Below c(*) the viscosity eta changes with temperature as usual, and the liquids are:Newtonian up to rates gamma of several thousand inverse seconds. Above c(*) the viscosity increases up to 1 order of magnitude as T is raised; shear thinning is observed within the entire gamma range under investigation. All experimental findings can be consistently explained in terms of micelles in which the S blocks are effectively hidden in the cores and the PBMA blocks form the outer shell. The inverse temperature dependence of eta stems from the expansion of the PBMA layers resulting from the improvement of thermodynamic quality of the solvent with rising distance from the miscibility gap of the system; the higher the temperature becomes, the more the coronae of the micelles penetrate each other and the more their relative movement is hindered.