Unless I switch the thermostat to the quot;offquot; position, the blower will kick on several times an hour for 10 to 30 seconds at a time and shut off. This is the first step. However, there is no pilot light and thus no heat. I believe that is something really simple; probably just a matter of flipping a switch. However, the switches are hard to find. Where are the limit switches and the flame rollout switch? It hasn't been serviced for more than 5 years now, so it just may need to be cleaned.
If it is an older furnace, it may have a thermal fan switch which won't turn the fan on until the heat exchanger heats up and then leaves the fan running until the heat exchanger cools down. This does two things-protects the heat exchanger from excessive heat and gets all of the heat off of the heat exchanger for maximum efficiency. First thing is check and/or change the air filter - make sure the vents are open and not restricted in any way. Both the outlets and return(s). I have seen what you are describing on this type of furnace (if you have a thermal fan switch). Usually the thermal fan switch either needs adjusting or it is going out of calibration. Look for a silver covered box half way up the front of the heat exchanger (it probably says Honeywell on it). Take the cover off and it will have a fan on, fan off and limit setting with little adjustment arms on it. Adjust the off tab slightly lower and the on tab a little higher. Don't touch the limit. Don't go crazy on your adjustments -adjust slightly. You may not have a thermal fan switch but a timed one so this is just a suggestion. If you have the model number, I could point you in the direction of a specific service manual for your furnace.
It sounds like it may be dirty and require routine maintenance. For more info including a maintenance guide and a troubleshooting guide, check out the furnace page at my source.
