Xchallenge won't start when ehgine is hot.

make, model, year? backfires are spontaneous burning (exploding) of unburnt fuel outside of the combustion chamber. suspect bad spark plug/s, ignition coils, ignition timing, computer, leaking fuel injector, etc. scan for trouble codes, then post back. because the problem is intermittent, problem manifests only when hot (engine at operating temperature) do tests for both cold & hot conditions. test resistances (ohm) of suspected sensors: cam & crankshaft position sensors, ignition coils (if possible),(search the web for the recommended procedures). also test voltages at the computer (search the web for the pin outs of the computer of your car). also check associated relays (like for the fuel pump, etc.) a bad relay may have its coil open when heated, then becomes good again when cold. i suspect the car may have a good fuel delivery but the sparks are not coming in on demand, thus backfiring.

My guess would be faulty spark plug lead.

is the check engine light on?

Replace the cam pickup in the nose cone on the right side of the motor. Due to heat cycles over time the epoxy melts and the wires fall out of the pickup. Pretty easy job to do, but you will have to reset the timing on the bike when you are done.

have you had the catalytic convertor back pressure tested. the symptoms you describe indicate a faulty convertor.

https://www.youtube.com/watch?v=yKFAmfeaycs

There is a proper way to start an engine. Most bikes have four controls to assist in starting.

• The choke, used when the engine is cold. Pull the red knob for choke.
• The " Hot Start " Lever, used when the engine is hot. Pull the lever to lean the fuel mix when the engine has been running.
• The de-compression lever, always used.
• The throttle, used to prime the cylinder.

Don't kick, instead, push the kick lever downward. You will feel the back pressure as the piston is going upward on the compression stroke to the point the pressure is great enough that the kick lever "locks up". You are very close to TDC. NOW, pull in the de-compression lever. Push the kick lever a little bit more to get the piston past TDC. Now release the de-compression lever. Give the throttle a 1/4 turn then let it snap closed. A diaphragm in the carb gives a shot of gas when this is done. DO NOT do this multiple times because you will flood the engine. Leave the throttle closed when kicking. A flooded engine will often backfire. Now give a strong kick through the full sweep of the kick start lever. Quickly get your foot off the kick lever at the end of the kick to avoid any chance of "kickback" from the kick lever. This happens in the case of a misfire, aka > backfire. It can be very painful, and can even break a leg. I am serious about that. Repeat the process (but without the throttle priming), until the bike starts. Go ahead and give it another primer shot after the 5th kick attempt. A good battery, a clean spark plug, a clean carb and clean air filter will also aid in starting.

check the fuel pressure

Check tightness of bolt where (carb/FI) goes into intake, and where intake goes into engine. Check gaskets in those locations, if any. Sounds like heat is causing some material to distort, causing a vacuum leak.