Your furnace is shutting down on limit. There can be a number of causes for this.
Start by making sure you have a clean filter in the furnace. A dirty or restrictive filter can cause this issue. Alternatively you could also have a dirty or plugged up A/C evaporator coil which is located above your furnace. This can also cause a furnace to cycle off on high limit, however is uncommon unless you have run your furnace without a filter for prolonged periods of time. Also if you have a high efficiency furnace, there is more of a chance to have the secondary heat exchanger plug up rather than the A/C coil.
You can also have a blower motor issue. The motor can be faulty or seizing up causing it to not spin fast enough to move enough air through the furnace. Another cause may be that you have a faulty limit that is opening prematurely.
The major issue that can cause this problem is a heat exchanger issue. If your furnace is cycling off on high limit, and everything checks out, you may have an internal blockage of the heat exchanger. If this is the case either the heat exchanger or the furnace will need to be replaced. A combustion analysis of the furnace is required to prove this is the issue.
If you happen to have a 2 stage high efficiency furnace you could have a bad ventor motor gasket which is allowing air to be drawn in behind the motor. Big cracks in the condensate collector pan can also cause this but is very uncommon. You can also have the a two stage gas valve high fire solenoid stuck open, but this is also very uncommon and can only happen on 2 stage furnaces. Also if you have a bryant, payne, or carrier high efficiency, you could have a cold spot baffle leakage that is allowing air to be drawn in between the primary and secondary heat exchanger however this is also very uncommon.
If you think your blower is not spinning fast enough you may also have a bad blower motor, or if an ecm motor, the control board may be bad. If its a fixed speed motor and your getting power to it but its not spinning fast enough it could possibly be a bad blower motor. If you decide to change out the blower motor, make sure to get the appropriate replacement capacitor to go with it. I actually did have the same issue on an older carrier high efficiency furnace a few weeks back. It ended up being a bad blower motor, however the motor spun freely and had no indications of seizing or hard starting.
High limits and you
A "high limit" switch protects the furnace against overheating and damage -- it's located in the output duct, or plenum, of the furnace and turns the furnace off if things get too hot up there. The usual cause of a high limit trip is inadequate airflow -- in your case, because an apparently faulty connection was causing the fan to not run.
If you continue to get the "electrical burning" smell after fixing the connections -- that's a sign the fan motor on your furnace is on the way out the door. Generally, you'll need to have an HVAC service tech come in and swap it for a replacement. (If you can access the other side of the connection, you can also use a voltmeter to measure the voltage drop across it -- anything more than a volt is cause for serious concern.)
Best Answer
I have replaced over temp switches in the past because the one that failed was no longer made. I used a slightly low temp rating as the exact temp was not available. Most over temp switches are manual reset. This is a safety so if there is something wrong you have to reset it by pressing a small button on the switch. Don’t replace with an automatic reset because this can damage the fire box and possibly start a fire.