NASA Funds Designs for a Nuclear Thermal Propulsion Rocket (space.com)
"Dangerous radiation. Overstuffed pantries. Cabin fever. NASA could sidestep many of the impediments to a Mars mission if they could just get there faster," writes Space.com, which reports NASA is now exploring an alternative to chemical rockets.
In August, NASA announced an $18.8-million-dollar contract with nuclear company BWXT to design fuel and a reactor suitable for nuclear thermal propulsion (NTP), a rocket technology that could jumpstart a new era of space exploration. "The strengths with NTP are the ability to do the very fast round trip [to Mars], the ability to abort even if you're 2 to 3 months into the missions, the overall architectural robustness, and also the growth potential to even more advanced systems," Michael Houts, principal investigator for the NTP project at NASA's Marshall Space Flight Center, told Space.com. NTP rockets would pull all that off by offering about twice the bang for the buck that chemical rockets do... "Nuclear thermal propulsion can enable you to get to Mars faster, on the order of twice as fast," said Vishal Patel, a researcher involved in subcontract work for BWXT at the Ultra Safe Nuclear Corp. in Los Alamos, New Mexico. "We're looking at nice 3- to 4-month transit times."
Almost correct. The temperatures are not actually hotter than a chemical rocket, but you can use pure hydrogen as fuel. Since hydrogen molecules are lighter than typcal exhaust gasses (water, CO2 etc), at the same temperature they are moving faster. That means you need less mass for the same velocity change in the rocket, or you can go faster on the same fuel.
The best chemical fuels are around 4500 M/s exhaust velocity. Storable chemicals are more like 3000 M/s. Nuclear thermal rockets get to around 10,000M/s So in principal you can go 2X as fast with the same fuel to mass ratio.
There are lots of caveats. The reactor is heavy. The radiation shielding is heavy - these both mean that you need a very large spacecraft before you have a net win in performance.
You probably don't want to turn one of these on before you are in orbit due to the potential problems with an accident (and the thrust to weight is pretty small anyway).
An additional problem is that its difficult to store hydrogen for long periods of time - you would need a complex and heavy refrigeration system. Or you can just use the nuclear rocket for leaving earth, and conventional storable chemicals for arrival.
Its a reasonable idea but with a lot of engineering tradeoffs that need to be considered. Its .... rocket science.