Sounds like stale air. Fungal problems can appear in less humid conditions than you would think. You couldn't hurt anything with a good fan or two to circulate air inside. Healthier than fungal sprays.

I have a fan in there wouldn't fungal problems show white on the leaves and trunk ?

Fungal and bacterial infections come in all forms. Moving air prevents too wet ,too long.
You might have your greenhouse too well sealed off from fresh air. Try and open the the vents on nice days and mix as much fresh air to dry out the excess moisture. And more fans strategically placed would help.
The best greenhouses or conservatorys make air circulation a top priority with good reason. You dont want a giant terrarium.

How warm does the palm stay in the day? It does sound like their environment might be the problem. I think I had a problem with them in a shade house when they were not getting enough air and heat several yrs ago.I would spray with daconil or Mancozeb just to be safe. You can try the combination fungicide/insecticide to make sure.