The physical and structural properties of cold-set whey protein isolate gels are largely influenced by the protein concentration and the denaturation conditions, namely temperature and holding time. In this work, we systematically varied the protein concentration, the temperature and holding time of denaturation in order to screen their impact on the resulting heat denatured whey protein isolate (HD-WPI) solution viscosity and gel elasticity. The gelation of the HD-WPI solutions was induced, at room temperature, through the addition of magnesium chloride. Based on the assumption that solution turbidity is associated with light scattered by protein aggregates, an aggregate concentration was computed for the HD-WPI solutions. For all experimental conditions, HD-WPI solution viscosities and gels Young modulus data fall, respectively, on two single curves when plotted against the computed aggregates concentration. Three concentration regimes corresponding to non gelling solutions, weak gels and strong gels could be identified. In this study was verified that cold-set gels produced upon addition of Mg2+ had a large spectrum of elastic properties.