Actually, things do thange with temperature, thus the term "Density Altitude"! The Hotter the air, the higher the density altitude, because the hotter the air, the thinner it is, which makes less lift. there are some places where experienced pilots will only fly into or out of early in the morning, or later in the after noon, when the air temprature is lower, and the effective density altitude is also lower!
Density altitude is a term that sometimes causes confusion to the uninitiated. A high density altitude is NOT a good thing. Density altitude is defined as the pressure altitude corrected for non-standard temperature variations. And while this is a correct definition, my definition is perhaps more appropriate: DENSITY ALTITUDE IS THE ALTITUDE THE AIRPLANE THINKS IT IS AT, AND PERFORMS IN ACCORDANCE WITH THIS COMPUTED VALUE.
Suppose an airport is situated at an elevation of 3,000 feet. It is possible with a low pressure system and hot temperatures for this airport to have a density altitude of more than 6,000 feet due to the effects of the pressure and temperature. An airplane operating at the 3,000-foot airport on a day with a 6,000-foot density altitude would have the performance normally found when flying at 6,000 feet during a day with standard conditions.