Here is an idea that may work.
Drill a small hole in one of the courses of the dome, maybe the sixth or seventh. Take a piece of metal tubing [maybe SS] with a cap on one end.
Drill a small hole in the cap and insert the tubing through the hole in the dome. The tubing should be long enough to extend to the outside of the dome. This length may be enough to minimize heat transfer by the tubing.
Connect the outside end of the tubing to a one gallon pump up style garden sprayer. There should be some sort of a fitting on the end of the tubing coming out of the dome to attach the rubber tubing from the sprayer.
Viola...
J W
