There are two possibilities causing the hot and cold air fluctuation depending on whether the air is hot like from the heater or just really warm like it is flowing in from outside.
If the air feel hot like from the heater then the problem is likely a damper door. There is often a damper door that switches position in the duct depending on whether you have the heat on or the ac. The actuator for the door can either be vacuum or electronically operated and can alternate like that between hot and cold if there is a vacuum leak or an electrical problem. One way to determine if this is what is causing the problem is to clamp off the heater hoses at the firewall under the hood. Or, get a piece of tubing and splice the two together temporarily. If the problem does not occur anymore then you know this is the problem. If the system is vacuum controlled then there is likely a vacuum leak that comes and goes (maybe a vacuum hose bounces as the car goes down the road and allows a crack to open and close, or a loose connection). If the system is electric then there might be a short, bad connection, or a bad actuator.
If the air only feels warm like it is coming in from outside then it is likely a problem with the fresh air door opening and closing. This could also be caused by an actuator problem like those above.
The first question we need to answer is why doesn't the blower motor work and the second is what is causing the door that you need to determine from above to act up like that. I'm suspecting either a fuse, relay, or the blower motor resistor is causing the fan to not come on. So the first thing to check is the fuses and relays. If those seem fine then remove the blower motor electrical connector and send 12 volt to it directly and see how it works. If it works good then I am suspecting a problem with the blower motor resistor. You will find this attached to the evaporator case (usually with a few screws) and an electrical connector going to it. The resistor actually protrudes into the evaporator case just downwind of the blower motor. Alot of times when the blower motor resistor is starting to go one or more of the lower fan speeds will not work. Note; on most cars the high fan speed setting is soley controlled by the relay so look at that carefully. I don't know the specifics of your car but I suspect that your actuators are electronic and that a problem with either the relay or resistor is resulting in the problem with the one of the door actuators.