Ryobi RY09440 4 cycle blow will run great for 10 minutes but then it will act like it is running hot and won't run at full speed. It runs with feathering throttle but stalls out if try to run at full speed.

this sounds strangely like the high speed jet/pathway in the carb is clogged up with something ,

the best way to fix it is dissasmbly and cleaning of carb in solvent , but ive also had some limited sucess in past of using car fuel cleaner (says on bottle "cleans as you drive") too

fuel pump going out and it will not run at all
coil problem will starteasy but fail after running for a while
fuel pump relay again it is running after starting and if the relay is no good , it will not pump fuel
try having the fault codes read first then have the faulty sensor replaced

Sounds like a lean condition. Rebuild carb, replace fuel lines and fuel filter and you should be ready to blow the leaves.

If it starts up after sitting for a few minutes, (like 2 or 3) it could have a plugged fuel filter or the gas tank strainer built into the fuel valve could be plugged too. Drain the gastank anyway and change the gas with fresh. can't hurt. If it takes 15-30 minutes or after the bike cools some I would look at an ignition coil. Check to see if it has spark next time it quits.

If your radiator is full of water, then its probably the thermostat sticking. The thermostat is located on top of the engine, under the housing that the radiator hose goes to

try running a good injector cleaner thru it- sounds as if you have a(or a couple)weeping injector,
try LUCAS injector cleaner- works on my sonoma

You probably need a slight carburetor adjustment. Try to turn the L mixture screw (the one near the bottom of the carburetor on the air filter side, closest to the engine) 1/8 to 1/4 of a turn counterclockwise. These mixture adjustment screws ( L and H) have odd heads on them and conventional tools won't turn them. I use an automotive type plastic wire connector (around 22 gauge) with a ring terminal end which I can hold. Tap the plastic end of the wire terminal connector onto the head of the screw with a small hammer and this will enable you to adjust the L screw. This adjustment will increase you high speed side and possibly allow it to run off choke in a regular manner.

spark plug or the coil/magneto

Replace thecarb screen, make sure you can see through the screen

yes , occassionally though it will run for full cycle ....but not very often