Because we can.
While this particular use case is stupid, with the exception of mildly conspiratorial Elysium-type assumptions, overcoming the problem of effective cooling in space is necessary for future space projects. This provides a testing platform for solving the problem.
I always wondered, why not have essentially heat batteries? You could use something like a heat pump to dump heat into a thermal mass for the short term. Maybe use those to power a Stirling generator in a central location? Be like stopping for gas, but also switching out your heat block? Or, maybe like a fuel pre-heater? Heck, you could even have just a high heat capacity material that you dump heat into and then vent superheated matter for fine control thrusters?