Active cooling: If you put the extra heat into fuel, you have a higher fuel flow per second at the faster speed so you can indeed cope with the higher heat flux

Active cooling: If you put the extra heat into fuel, you have a higher fuel flow per second at the faster speed so you can indeed cope with the higher heat flux and enjoy the lower total heat quantity. Passive cooling: If you have to radiate the heat away , then the surfaces will reach a steady state relatively quickly and you have to deal with the flux. If you burn up in two minutes it doesn't help you that the flight would only last two hours. You can't carry heavy heat sinks in an aircraft.