The blower has been working fine for years until recently it started to cut out from what appears to be overheating (only a guess).
I said that because it would not restart until moments later, like 20 minutes (possibly after it has cooled down).
I have recently changed the oil, not sure if I also need to change the spark plug, but does that sounds like a spark plug issue?
Overheating an air-cooled small garden tool engine is unlikely. The problem will most likely be either with the fuel feed or electricals. Changing the spark plug is certainly worth doing, just in case this is failing.
Have you replaced/repaired the fuel cap recently? These need to have a working 'breather hole', without which as the fuel level drops, a semi-vacuum is created in the tank and the fuel feed to the carby stops. This problem matches your symptoms, as after a break the air pressure in the tank comes back to normal and the engine will restart and run OK until the vacuum builds up again.
Using a carby cleaning aerosol spray wouldn't be a bad idea too, in case deposits are building up and blocking the tiny jet inside.
You could also check/service the air cleaner, while you're at it, as blowers operate in a very dusty environment and the engine may be struggling to breathe.