Yes, it is a gas furnace. There are 4 such units for the house.
Yes, it is a big house, but the cost of living here is cheap. I am
out of work for a long while, so really tight with money. We bought
the house when we both were working and got a great deal on it.
I checked the vents and they all seem open and unobstructed (ceiling
vents). I can feel a bit of air coming out, but don't know if that is
enough.
I changed the air filters.
The room that is problematic is downstairs.
I swapped out the high limit switch with another one, just to make
sure that the one there was not faulty.
The other one (from an upstairs unit) is
Texas Instruments
pat no 5144273
1NT17L-1875
L160F-30
025-29041-004
9413

It shuts off 10 deg F colder.

Maybe I should try to find one that cuts off at 180F

I watched the unit with the cover off.
It seems to work fine just fine for the first 10 mins.
The furnace turns off after 5 min, presumably when the high limit
switch protects the unit from over heating.
It blows air for about 2 mins, and reignites and heats up and shuts
down.
It seems to operate, but its just that after a while it stops heating
up.
I have the thermostat set at 74F, while as it only gets up to 68F.
It seems to behave as if had reached the desired temp.
Maybe I should check to see if there is still a call for heat by
seeing if there is current across the C-Y leads [call for heat by the
downstairs thermostat.