My understanding is that IR signature considerations make any direct air cooling, or heat exchangers venting overboard, problematic. The approach taken is to dump all heat into the fuel and thence into the primary exhaust, which is managed and mixed-flow in cruise. The heat either goes out as fuel is burned or goes through an HX in the inlet duct - that HX is fed through a small inlet above the right main inlet.
The heat sources include the cockpit and avionics ECS and the flight controls -
AFAIK the aero loads on the controls are opposed by the electrohydraulic actuators, and that generates heat (whereas a pure hydraulic system is more thermally balanced). Correct me if I am wrong, Engines.
Under certain circumstances more heat is generated than can be got rid of and the fuel gets hot, and will eventually hit limits. (There was some work done on heat-tolerant fuels some years ago, but the F-35 has to use regular JP-5 or JP-8.) This could mean that you'd have to go into a less demanding part of the envelope to cool off, or retain some part of the fuel load.
Clearly though the heat capacity of the fuel is affected by how hot it is when you load it. Fuel chillers were used for early flight tests. The new fuel pump was more efficient (=added less heat to the gas) but apparently the Luke folks were seeing an issue, came up with a cheap mitigation and went public with it.
By the way, it would not necessarily mean cancelling sorties, so that's a potential misdirection. One obvious mitigation would be to launch with part fuel and then top off from a tanker that's been chilling at FL250 for a while.