I had a similar problem on a K series caterham, that didn't like to start when the engine was hot. Being a passenger on a track day with my son facing oncoming traffic at Brands following a spin, reminds you why you need a reliable starter!
It was finally tracked down to the starter not being exactly square to the flywheel and ring gear this was exaggerated when hot, effectively jamming the starter. Being tucked up under the exhaust manifold, didn't help either. A high torque replacement and some fettling of the mounting flange to square it up, solved the problem.
Not spinning also helps