I own a rental property that is 80 years old. I'm currently having a fan installed to remove moisture from the first floor bathroom. .

While the electricians were in the attic they alerted me to the fact that ice had built up in the attic. The ice is built up on the north side of the house directly over the mentioned bathroom. The fan was being installed due to the high humidity in the bath.They are going to route the exhaust pipe out the gable end

the particulars and question:

- 1000sf house with gable ends, new roof installed with 4 roof vents,
- no sofit or overhang to speak of,
- minimum insulation (had a contractor say it wasn't worth adding more for a rental), has a rockwool type insulation that covers the joints.
- All rooms in the house have some form of cracks in the ceiling plaster.

???

What all am I going to need to do to solve this problem? Also, what do I do about the ice that has formed?
my thoughts:
- I plan on going up into the attic and search for and plug any visible gaps in the insulation to minimize heat lost from below.
- Additional insulation could also be added.
- fill ceiling cracks, repaint the ceilings with oil based paint