Heat uses the National Weather Service’s heat-index categories, applied to the modelled feels-like temperature: Caution 80°F–90°F, Extreme Caution 90°F–103°F, Danger 103°F–124°F, Extreme Danger 125°F and up.
Air uses the US EPA air quality index: Good 0–50, Moderate 51–100, Unhealthy for Sensitive Groups 101–150, Unhealthy 151–200, Very Unhealthy 201–300, Hazardous above that. The number here is that same EPA index, computed by Open-Meteo from the Copernicus CAMS model.
Each hour takes the harder of the two constraints, and the strip says which one. A “best window” means hours where the feels-like temperature stays below 80°F (below the NWS Caution band) and the air is no worse than Moderate — the EPA’s general-population activity cautions start at 101. No thresholds on this page are ours.