We report on a comprehensive investigation of the flow behavior of colloidal thermosensitive core-shell particles at high densities. The particles consist of a solid core of poly(styrene) onto which a network of cross-linked poly(N-isopropylacrylamide) is affixed. Immersed in water the shell of these particles will swell if the temperature is low. Raising the temperature above 32 degrees C leads to a volume transition within this shell which leads to a marked shrinking of the shell. The particles have well-defined core-shell structure and a narrow size distribution. The remaining electrostatic interactions due to a small number of charges affixed to the core particles can be screened by adding 0.05M KCl to the suspensions. Below the lower critical solution temperature at 32 degrees C the particles are purely repulsive. Above this transition, a thermoreversible coagulation takes place. Lowering the temperature again leads to full dissociation of the aggregates formed by this process. The particles crystallize for effective volume fractions between 0.48 and 0.55. The crystallites can be molten by shear in order to reach a fluid sample again. The reduced shear stress measured in this metastable disordered state was found to be a unique function of the shear rate and the effective volume fraction. These reduced flow curves thus obtained can be described quantitatively by the theory of Fuchs and Cates [Phys. Rev. Lett. 89, 248304 (2002)] which is based on the mode-coupling theory of the glass transition.