Have you checked the temperature inside the furnace? It is possible the pilot light went out.
Disclaimer: I don't hold any special knowledge about furnaces. They are dangerous if tampered with. Re-lighting pilot lights can blow your house up. I don't recommend anything.
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.
Best Answer
NEVER JUMP A LIMIT SWITCH TO ALLOW A GAS APPLIANCE TO RUN. THIS IS ONE OF THE MOST IMPORTANT SAFETY IN THE SYSTEM AND IS REQUIRED FOR PROPER AND SAFE OPERATION OF THE UNIT.
Limit switches may only be jumped by technicians to test and rule out certain components and are not to be left bypassed.
Your furnace seems to be going off on High limit. When the fan runs for long enough after the furnace shuts down on high limit, it will cool the limit switch to the point where it can close again and re run the heating cycle. This is why the unit is cycling.
There are many things that can cause this. Listed in order from most common to least common:
Always check your furnace filter first. This may save you the cost of a service call. If your filter is clean then have a licensed HVAC service technician look at and repair the unit. This problem will either be a very very minor issue, or a very very major issue.