Cycloolefin copolymers of ethylene and norbornene, with norbornene content in the range from 36 to 62 mol %, were studied with respect to the thermal, thermodynamic, and rheological properties using differential scanning calorimetry, pressure-volume-temperature, and dynamic mechanical measurements. All copolymers obey the principle of time-temperature superposition, i.e., they can be considered as thermorheologically simple except for a temperature range in the vicinity of T(g). Despite this, the results on (i) the ratio of activation energies E(V)(*)/H(*) used to quantify the origin of the liquid-to-glass transition, (ii) the pressure coefficient of the glass temperature T(g)(P), and (iii) the dynamic fragility m suggest increasing dynamic heterogeneity with increasing norbornene content that is driven by the structural heterogeneity along the backbone.