**Yes—78°F at 105–106°F outdoors is achievable with a properly sized, functioning central AC and a reasonably insulated home.** Whether your particular system should maintain it depends on the home’s heat gain and the conditions the system was sized for.

AC sizing uses a **local outdoor “design temperature.”** Above that temperature, a correctly sized system may run continuously and still let the indoor temperature rise. ENERGY STAR recommends using the local temperature exceeded during only 1% of annual hours for cooling-load calculations. [ENERGY STAR sizing guidance](https://www.energystar.gov/partner-resources/residential_new/working/hvac/hvac_designers/design_temp_limits)

Your **89°F indoor temperature with a 78°F setting warrants investigation.** Those readings alone can’t establish whether the cause is inadequate capacity, heat entering the house, or an equipment problem. The warmer overnight low could also have left the building holding more heat going into today.

There’s no universal outdoor-to-indoor temperature difference an AC can maintain. The commonly mentioned **15–20°F temperature drop refers to air passing through the indoor cooling coil**; the actual drop varies with humidity, airflow, and equipment. [ACCA explanation](https://hvac-blog.acca.org/a-split-in-diagnosis/)

Useful checks:

- **Check the filter and airflow:** replace a dirty filter and keep supply and return vents clear.
- **Observe operation:** when the house is well above the setting, check whether the outdoor unit runs continuously and whether the vents deliver cool air.
- **Reduce solar heat:** close blinds or curtains on sunny windows and keep vegetation and debris clear of the outdoor unit. [Trane heat-wave guidance](https://www.trane.com/residential/en/resources/blog/prepare-hvac-for-summer-heatwaves/)
- **Arrange service if it continues reaching the upper 80s:** ask for checks of cooling performance, airflow, refrigerant charge, and duct condition. If the equipment performs correctly, ask for a Manual J load calculation to assess its capacity for your home. [DOE diagnostic guidance](https://www1.eere.energy.gov/buildings/publications/pdfs/building_america/measure_guide_air_cond_diagnostics.pdf), [ACCA sizing methods](https://www.acca.org/acca/standards/technical-manuals)

Your city, whether the AC runs continuously, and whether it reaches 78°F overnight would help narrow down what to expect.