**In normal, steady operation, air at the vent should not be 10–15°F colder than the air leaving the evaporator coil.** Your doubt about those readings is reasonable, but the discrepancy alone doesn’t establish which contractor’s diagnosis is correct.

The evaporator removes heat. After that, ordinary ducts provide no further refrigeration; air usually gains heat on its way to the rooms, especially through ducts in a warm attic. [DOE’s duct guidance](https://bsesc.energy.gov/energy-basics/hvac-sealed-and-insulated-metal-ducts) describes this heat gain.

Several things could explain the reported numbers:

- **Different kinds of measurements.** An infrared “temperature gun” measures surfaces, not the air flowing past them. A reading aimed at a register or air-handler cabinet therefore isn’t directly comparable to an air-probe reading. Surface material and reflected infrared radiation can also affect the result. [FLIR explains how infrared thermometers measure temperature](https://www.flir.com/en-gb/discover/professional-tools/infrared-thermometers-101/).
- **Different parts of the airflow.** Air immediately downstream of a coil may not be uniformly mixed. One probe could sample a warmer stream while a duct branch receives colder air. The air hasn’t become colder along that branch; the measurements sampled different streams.
- **Different times or locations.** Cycling, insufficient time for the thermometer to settle, or a probe touching warm metal can distort the comparison. Also, “above the coil” means downstream only if the air flows upward.

**A dry register surrounded by warmer room air cannot, at steady state, be colder than all the air cooling it without some additional cooling mechanism.** Evaporation from a wet register or a register still cold from an earlier operating condition are possible exceptions. The pressure drop through an ordinary residential vent cannot explain a 10–15°F reduction.

The useful next step is to have the technician compare **air temperatures with suitable probes**, during the same continuous cooling run, at the coil’s downstream side and inside the supply register, keeping the probes off metal. Sampling several positions downstream of the coil would check for uneven temperatures.

Neither “55°F at the handler” nor “low 40s at the vent” alone proves the system is healthy. Those readings need context, including entering-air temperature, humidity, and airflow.

This fits a home-improvement/HVAC question well; moving it to Physics SE isn’t necessary.