I cant really speak to longevity or cooling.... but comparing driving characteristics at Hockenheimring, Nurburgring GP, and Nurburgring Nordschleife, the handling feel of the 2018 M2, M2C, and M2CS (Hockenhiemring only) feels very similar in stock form and I submit that after a lap or two on track its hard to notice any stock to stock handling difference. Looking at the corner speed telemetry, they are so similar, I couldn't tell a difference between cars lap to lap.
The obvious major difference is the engine, and I would rate the feel in power jump from OGM2 to M2C, and M2C to M2CS as feeling like similar evolutions. It is certainly noticeable, but if chasing lap times I think there is better return by improving handling.
To compare extremes, here is a speed trace down the long Parabolika straight at Hockenheimring M2 vs M2CS (M2C as expected falls in the middle). Acceleration is similar until about the 3-4 gear change, then the M2CS walks away and the DCT changes are very (un)noticeable. Surprisingly (to me), I have found similar acceleration speed traces to about 100mph between M2/M2C/M2CS.
These traces were on very hot days (about 95deg ambient), and IAT telemetry from my OGM2 was 167F at the end of the straight. I felt the M2CS was pulling timing, too. On a cooler day I constantly got about 4-5mph faster at the end of the straight in my OGM2 with IAT closer to 130. Both were completely stock engines.