Is there any reason to leave the engine running while doing hand work?
No! In fact some localities are requiring no more than 5 minutes of idle at any time.
Maybe if you've been running it hard enough that you want to let the turbo cool down before shutting it down, or if the starter is questionable. Otherwise, better for the engine not to idle.
Letting the engine idle for extended periods will lead to excessive engine wear and fuel consumption.
Unburned fuel deposits settle in the hone marks on the bores which creates a glazing around the bore causing excessive blowby, excessive oil consumption and can leave carbon deposits on top of pistons which can lead to pinking/pre detonation and hot spots aswell.
Engine idle especially on a diesel is a killer. Seen many engines when I was over the road that were sent to an early grave because operators would leave them idling all night. As Delmer said if your idling for cool down then fine but other then that shut it down, unless of course your trying to justify getting a new engine
Only fair to mention one should idle a cold engine for 2-5 minutes of warmup. This may not be the case so much with newer engine due to improvements in metallurgy. But I prefer to idle up and idle down for three to five minutes. With a trackhoe, I usually do some slow movements with the boom and the swing to warm the hydraulic fluid in cold weather, especially before traveling. I have seen a travel motor seal blow out when the operator took off in below freezing temps without a warmup. JMHO. Perhaps on the newer stuff with computers onboard, hydraulic flows are regulated to avoid these problems in cold weather.
Hell yes , heat or AC.
This is where it gets interesting on engines IMHO. Engine temp >160F (175F) oil pressure is good, You will be fine. I was the first one of three that day to blow oil seals on the cooler (where the foreman said their not) I was exercising it to warm it up -28C. How dirty is the rad I have seen where they hardly cool at all they are so dirty( I am the temp operator) This pickup's transmission doesn't want to shift till >86*F unless you throttle the cold engine.
Some newer electronically controlled engines don't allow this, but if I do have to idle for any length of time I idle it up to about 1000 RPM to help burn the fuel.
I'm old when I was much younger you never shutdown the engine for short periods of time like lunch they had pony motors, on old dozers you placed the transmission in neutral and engaged the clutch to protect the throw out bearing. Some the gippo outfits the electric start Euc's and Terex's didn't have batteries but was maybe fun times. At least not every bone in my body hurt but then again that maybe the reason they do