The reactor is at 1900 degrees
Hi gb
The super-performance you're expecting from an NTR only happens at temperatures of over 2300 K - at that temperature the Vex is 7.5 km/s. To get 8 km/s requires about 2500 K. But the whole system is cooled by a high mass flow of propellant - likewise Zuppero's water rocket.
So don't worry, be happy ;-)