Furnace Trips

your likely best off to get the furnace serviced by a pro. espically if this is a 90+ furnace.

highly complex and technical, and a malfunction could freeze your pipes

Sometimes an indoor fan motor or its capacitor if it has one will overheat and stop running only to come back on again when it cools.

Which safety is tripping? Is it a high limit safety switch?

TDD

Golly, what kind of furnace is it? Gas, oil, coal?

And that's the brand, not the model.

I don't think you know enough to say it tripped at the completion of the heat cycle. You just know it ran a while before tripping.

You need to post more specifics like type, brand, model to get better advice.

Safeties tripping are ether because what the are designed to trip on is happening or they are tripping falsely. You need to watch it and when it trips see what the conditions are.

You can watch and you can hear the thermostat operation !! If it coincides with the furnace, then it completed cycle. A furnace could still overheat near end of cycle, depending on temps.