For the cold start valve, it is highly dependant upon a properly-working thermo-time switch. According to the DJet manual, the time it is injecting "reaches zero" between 20° and 40° C. This means, with a properly-working switch, if your coolant is as warm as 40°, the cold start valve may still be turned on. If the switch is bad and is in the closed position at coolant temps of say 60°, which is definetly possible with a 30+ y/o switch dependant upon a bimetallic strip, then it will cause hot start issues.

The aux air valve, according to the DJet manual, should be completely closed between 60° and 70° C. If it's still allowing air to flow through it at operating temp, and idle speed was set thusly, then that can be a major part of the problem. Of course, it's more likely that you have a bad thermo-time switch or water temperature sensor, as this would give harder cold starts, not hot ones.