In fresh/hard cheese manufacture, a high casein concentration is desired, whereas, for quark production, a high total protein concentration and a high degree of whey protein denaturation is needed. However, concentration impacts inevitably the concentrate's viscosity—particularly after heat treatment. Our research question was therefore, which mechanisms are responsible for changes in viscosity upon increasing the total protein concentration, varying the casein/whey protein ratio, and heating. In order to answer this question, we investigated the viscosity of unheated and heated milk protein concentrates (3–14% total protein) and three casein/whey protein ratios (85:15, 92:8, 98:2). It turned out that a 37% whey protein depletion was sufficient to 1) inhibit the impact of the casein micelles' repulsive forces on the viscosity; 2) achieve the highest polydispersity and, therefore, particle packing density of all concentrates; and 3) allow up to 95% whey protein denaturation without changing the viscosity of the concentrates after heating.