What does this problem sound like?
There is a 25 year old gas furnace in the house we rent. (The guy that owns the place claims there is NO problem at all. He said the igniter is brand new and working fine.)
It blows cold air for the first 10 minutes of each heating cycle. (Sometimes this happens for 30-60 minutes.) Then heat starts to appear fine.
The "blowing cold airs" periods eventually get shorter and shorter... as the "blowing hot air" periods get longer... and eventually, after 3-4 hours, the home is at the desired temperature.
Perhaps a thermostat problem?
Does the average thermostat independently control the "on/off fan" and the "on/off flame" events?' Perhaps the "flame on" part of the thermostat is bad or incorrectly adjusted?
Perhaps a furnace problem?
Is there some timer-device that decides how long to wait between "fan on" and "flame on" events?
Perhaps this delay is set too long? Or the device is bad?
Another (perhaps totally unrelated) thing:
The problem seems worse when the furnace is trying to heat the place from 60 degrees, up to a thermostat setting of 70. (Yes, it gets THAT cold in here sometimes.)
It seems to happen less often... when trying to heat the house from 75... up to a thermostat setting of 85. (Yes, have to set things VERY high, to lessen this problem.)