It is good practice for all engines should be warmed up & cooled down.
Warm up before asking the engine to do hard work - I usually run at high idle for a few minutes before working an air cooled engine (longer for a liquid cooled) engine. This gets all those separate bits of metal to expand to close to their working limit and brings the oil up to temperature for best circulation.
Cool down. This is not so much cooling, as stabilising/bringing the engine temperature (again all those bits of metal & the oil) down to a lower/non load steady temperature. Again I run the engine at high idle. High idle gives good air & oil flow for a nice consistent all over temperature drop. For a mower, I usually do this, while using compressed air to remove all the chaff from around the mower, paying special attention to transmission/engine cooling fins.
I do this for my 2/ as well.
Except in an emergency NEVER intentionally shut down an engine operating at full rpm.
