Which overheating equipment terminated the record-breaking fusion reaction at the JET reactor? It has been reported in Nature that in December 2021 the Joint European Torus (JET) fusion reactor near Oxford in the UK sustained a 5 second fusion reaction and produced a new record for fusion energy production.
The Guardian newspaper reported that the reaction was only stopped because some of the equipment got too hot.
My question is: What was the equipment that overheated and what makes it difficult to cool?
 A: It's hard to answer your question before the full details of this work are published, but my guess is that they are talking about the neutral beam injection (NBI) system. This is one of the systems that is used to sustain the reaction and, in this article the author's mention that it's (over)heating is the main limitation to JET pulse duration.
Essentially, the NBI system produces a beam of very energetic neutral particles that are injected into the plasma (the fuel). The high energetic neutral particles undergo charge-exchange reactions in the plasma and then give off their energy to the plasma particles through collisional processes, so that the plasma is kept at the necessary high temperatures for fusion reactions to occur. Before this happens, the beam is accelerated and fed through a beamline that leads it (in)to the plasma.
This beamline heats up during operation of the NBI system, and in this article the authors explain why. Essentially, even though the beam is focused inside the beamline there are still highly energetic 'fringe particles' that collide with the beam line wall and heat it up. Moreover, reionization takes place between the neutral particles and traces of background gas in the beamline. These high energetic ions will deflect in the gradient of the magnetic field as the beamline approaches the tokamak, and they will deflect against target plates around the tokamak port hole. The power flux these target plates receive is significant (more than 5 MW/m$^2$), which can only be sustained for a limited time before they need to be cooled.
A: 
My question is: What was the equipment that overheated and what makes
it difficult to cool?

The primary confinement magnets. They are simple copper-wound electromagnets so they heat up during the experimental run due to the huge currents being dumped into them.
As the design was not ever going to be able to run for a long time, all the rest of the equipment was designed to the same criterion. There's no point in having enough power supply so the induction coil runs for 30 seconds if the magnets can only run for 5. Basically, everything in the design ultimately runs for a few seconds.
