This is why places like DIA, for example, have very long runways. If you calculate the density altitudes you'll actually find that even at 120*F in Phoenix, the air density is the same as DIA on a cold day.
Altitude of Phoenix is 1086’, and using a temperature of 120*F, standard altimeter setting of 29.92 inches Hg, and dew point of 68*F (doesn’t really make a difference), the density altitude is 5359’.
DIA/Denver is at 5280’ elevation, it has a density altitude of 5359’ at about 38*F! On a decently warm summer day (75*F) the density altitude is 7828’.
According to Wikipedia, the runways in Phoenix are 7,800 to 11,489 ft compared to DIA which are 12,000 to 16,000 ft.