We present evidence that co-solute (glucose syrup) can cause massive changes in the time/temperature dependence of structures formed by K-carrageenan. Modest concentrations of glucose syrup ( < 40%) promote conventional disorder-to-order transitions of its hydrogels and reinforce the final network strength, as seen by small deformation dynamic oscillation. In contrast, at higher concentrations of co-solute, there is a leap in thermal stability which is associated with a drop in network strength. Differential scanning calorimetry demonstrates that the rise in network strength is accompanied by more pronounced enthalpic events, but the change in enthalpy declines in accordance with the drop in storage modulus at higher levels of co-solute. Cooling of the samples triggers a transformation from low modulus solid-like to high viscosity liquid-lice behaviour and at 85% cosolute, shear moduli increase by about five decades. Eventually the storage modulus overtakes the loss modulus completing the progression from the rubbery plateau and glass transition region to the glassy state, in the way reported for amorphous synthetic polymers. Vitrification was equivalently followed by changing the temperature or frequency of measurement thus implementing the time-temperature superposition principle. The Williams-Landel-Ferry/free volume theory was operative in the glass transition zone, thus allowing calculation of useful parameters, e.g. the thermal expansion coefficient, but it gave way to an Arrhenius relationship for the relaxation processes in the glassy state. It is proposed that the addition of co-solute induces a transformation from an enthalpic aggregated structure to a partially cross-linked structure of more flexible chains where the entropic contribution to elasticity becomes dominant, thus allowing vitrification of the polysaccharide network.