The blaze was sparked at Mortonhall Crematorium yesterday after a cremating unit overheated and set the roof alight.
It is understood that no human remains were in the cremator at the time. Six appliances and more than 25 firefighters tackled the blaze for six hours.
It is the second time in just over two years that the same crematorium has suffered a serious roof blaze.
Sections of the roof above the furnaces needed to be cut away in January 2004 after a blaze started, although the cause was unclear at the time.
An investigation was under way today into why the fire started and the extent of the damage.
A spokeswoman for Lothian and Borders Fire and Rescue Service said: "We were called to the crematorium to deal with a fire in a cremating unit. It had overheated and caused insulation on the roof to ignite.
"Firefighters cut away the timbers on the roof to contain the fire and used three pumping and three specialist appliances to extinguish the flames. Part of the roof was also cut away as a precaution."
A council spokeswoman said: "Assessment of the resultant damage is under way with support from Lothian and Borders Fire and Rescue Service and from the property care staff of the Council's Services for Communities department. Officials wish to reassure families that there will be no disruption to funeral services."