I don't think there are any coolants that would be appropriate for life's temperature ranges at the right pressures that can be synthesized biochemically.
I don't know about the other part (temperature/pressure).
Sweat is an open heatpump loop. You're intending a closed loop of course in your comment, but same process.
It isn't though, because powered mechanical compression and decompression is what allows a heat pump to outperform the inherent thermodynamic limit of evaporative cooling.
Is that possible? Could there be a biochemical equivalent of a Peltier junction?