Massive radiators. The ISS has radiators that have a dissipation capacity of about 3m^2/kW. If we use that number, we'd need a 3000m^2 radiator per megawatt, which is the scale they're talking about. This could theoretically be brought down, but not even by an order of magnitude.
I wonder how much cooling the solar panels alone would need, when operating at that scale.
You cool the fluid by flowing it through the radiator. The radiator emits heat radiation into space and cools down the fluid. As long as the fluid is hotter than the equilibrium temperature of the radiator (determined by radiator, space and sun radiation), it will emit more energy than it receives and cool down the fluid.
I wonder how much cooling the solar panels alone would need, when operating at that scale.