TotalBeginner I think not...
I've had quick look at various check-lists (POHs) for the Archer and most them seem to say 'Prime as required' - not very helpful! So why is a hot engine difficult to start? This is probably due to a vapour lock; once had a Renault car that suffered this problem. The Renault fix was to allow the cooling fan to run on after the car engine was turned off thus cooling the system down; the fuel line ran over the top engine. You can disregard the impulse mag selection because its not selectable - just turn the key. Another thing I've tried is to fully open the throttle and crank until the engine until it fires and then quickly retard the throttle.
There was a theory with fuel injected engines that you could close the throttle and run the electric fuel pump, this would pump fuel through the system, the unused fuel being returned to the fuel tank. The idea being to cool the fuel system down and eliminate the vapour locks. I only mention this as this indicates again that the problem seems to be with the dreaded vapour lock.
So a Black Art.