[euromodder]

If it's actually too cold on your butt, use what nature uses in the bloodstream to your hands and feet ...
A heat exchanger between the cold flow and the returning warm flow

This will
- warm up the cold stream going to your butt ; the size and efficiency of the heat exchanger will determine your butt temperature
- cool down the return flow, reducing the melting rate of the ice

Remember, cooling is more efficient (or as here: too efficient) as the temperature difference is higher
By increasing (!) the coolant temp @ your butt to a more comfortable level, you'll actually increase the time the system can keep you cool ...