Craftsman GT5000 W/22hp B+S surges and dies when warm

check you MAP sensor.

This sounds like a choke issue. Do you have a choke on that engine?

The purpose of a choke is to allow for a varying air:fuel ratio depending on how hot the engine is. A cool engine needs a more rich mixture of fuel to air. Once the engine warms up, it runs best with more air. The Choke is a mechanism that allows the operator to manually adjust this mixture. Generally, the choke is closed to start a cold engine, then is opened in 2 or 3 stages as the engine warms up. As the operator, as the engine starts to run smoothly, you would actuate the choke to the next notch, changing the fuel:air ratio so more air is mixed in with the fuel. It's probably best to give the engine a few minutes to warm up while you progress through the choke stages until it's fully open providing the best mixture for operation prior to beginning to clear the snow.

If you follow that process and the engine stalls when the choke is opened, then you need to clean your carburetor.

Think about what you just said. Only does this in times of higher temps out BUT never in winters cold. Doesn't that seem strange to you. Well I guess it does, huh. Anyway, know these systems helps. When engine is started, the temp sensor tells the computer it needs to place the engine to cold start mode. It does this and extra fuel is put into the cylinders to keep it running like a choke on the carbureted engines. But those you can turn the choke off or it does this automatically from the warmer engine. If in fact the temp sensor is not telling the computer it's warm enough to be taken out of cold start mode, it keeps dumping excessive fuel into the cylinders an flooding the engine causing it to surge and then die, because it's flooded. Therefore, the temperature sensor is faulty and needs replaced. Do that and drive on.

88 ford ranger 2.9 surges buck down when take off in first gear

Clean the throttle body bore and plate of any carbon and the Idle Air Control may be going bad .

Carburetor possibly needs cleaning. Initially, remove air filter, start mower and while it is running, spray some aerosol carb/choke cleaner into the carb thru air intake area. Continue doing this several times but not too fast or heavy to make it stall and then spray it heavily until engine dies. Let it sit for several minutes and then try a restart. If no difference in performance is noticed, carb may have to be removed and cleaned in bath-type cleaner and governor settings will need to be checked also.
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clean out the carburetor jets re-assemble then adjust fuel mixture screw until it runs correctly

The idle problem sounds like an idle adjustment. The surge may be the throttle cable, try spraying a lubricant from the top of the cable and work it back and forth to loosen and release any debris.

I had the same symptoms on my 1993 F-150. A friend of mine commented that he could smell gas in the exhaust. Eventually, it got to where it would start, then die after a few minutes and wouldn't restart after that (at least for several hours). It turned out to be a bad fuel pressure regulator that was causing it to flood. It was about a $25 part and an hour labor to replace (not difficult, just awkward getting to the hex head bolts).