Establish what actually stops
Tell the technician whether the burners stop while the fan continues, whether all operation stops, and whether a code appears. Record the thermostat's normal user display and the timing you already noticed. Do not force second stage, open the cabinet during operation, or repeatedly reset the furnace for testing.
A symptom tied to the higher stage narrows the investigation. It does not identify a failed temperature limit, gas valve, pressure switch, or control by itself.
Request a check in both stages
Ask whether the technician verified the staging configuration, thermostat signals, blower setup, gas input, and the relevant operating limits in both stages. Temperature rise means how much warmer the supply air is than the returning air. It needs to match the equipment's specified range.
For example, Lennox's EL296UHE instructions call for a stabilized second-stage temperature-rise check and warn that an incorrect setting can cause erratic limit operation. This is an example of the professional check, not a procedure or range to copy to another furnace. Lennox EL296UHE operating checks.
Ask how airflow and any measured pressure resistance compare with the model's requirements. If the air path requires changes outside the service provider's scope, identify the qualified responsible party and complete cost before choosing the repair.
Distinguish a protective response from a failed control
Carrier explains that a limit protects against overheating and that restricted airflow can cause a trip. A new switch cannot establish that the heat and airflow are properly balanced. Carrier limit-switch guidance.
Ask what evidence shows the control itself is defective, if that is the recommendation. Do not request a more permissive limit or accept one simply because it makes the burners stay on.
If another stage-specific fault is confirmed, ask how the proposed repair addresses it and what operation was verified afterward. If the cause is still unknown, get clear guidance about keeping the affected equipment out of use. First-stage-only operation should not be a homeowner workaround chosen without qualified guidance.
Your next step is to report “fails only in higher heat” and ask for a diagnosis that covers both stages. Keep the written operating findings and the repair recommendation together so you can see why the chosen work fits.