I have a Honeywell TH8000 thermostat.
Is there a possibility to control the delay before the auxiliary heat source switches on when I ask for a higher room temperature?

Yes if you change the stat to economic instead of comfort in the installer setup. Also you can get a out door temp sencer and have a aux lock out where you can put a certain temp in so that the aux will not come on inless the outside temp is lower then your lock out. And you can also change the aux cycles per hr whitch will not let it come on as many times.