IIRC the wast majority goes out with the propellant & propelant being cold liquid hydrogen also helps. Still after a burn you would definitely need some coolin

IIRC the wast majority goes out with the propellant & propelant being cold liquid hydrogen also helps. Still after a burn you would definitely need some cooling until the fision byproducts decay. How much & for how long I have no idea. If a couple minutes/ hours just running some more hydrogen through the shutdown reactor might be enough. Otherwise passive or active cooling loops and radiators could be needed. Or maybe not enough fission byproducts form during the tens of minutes the reactor is active and cooling after a burn is not a major concern?