The favored temperature range for companion parrots is 65 to 80 degrees Fahrenheit. It's a preferred range that encompasses the full range of companion parrot breeds. In our home the range we live in is 69 to 76. Generally. The house has dipped to the mid 60s at times during the winter when I am too cheap to turn on the heater. (Yes we Florida folk can be big babies with cooler temps, or maybe it's just me that's a big baby.)
Companion Parrots can handle the extremes of 40 degrees Fahrenheit to 95 degrees Fahrenheit for periods of time. These are big variable ranges and are affected by many physical variables of your parrot and their environment.
Three factors that affect tolerances are air movement, parrot body weight and acclimation.
Air movement is a huge key to handling the higher temps. The more fresh air movement and ventilation the better high temps can be handled by a parrot. Ventilation and moving air assists in cooling a bird's respiratory system and that assists in keeping their core temperature from rising. It's that moving air and a bird's ability to modify itself that controls the core temperature issues. Air movement and the ability for a parrot to get to the air stream of movement is critical. A panting parrot with wings open is working on controlling that core temperature. Of course signs of duress like quick short panting, drooping body/shoulders, wings open, and soft eyes mean he's loosing that battle and needs to be attended to immediately. Adding a mist of water to a source of air movement can also aid in core temperature controls. Companion Parrots handle cold far better than heat. If you see a parrot in distress please alleviate the issue immediately. Stagnant stuffy heat is a serious threat to parrots.
A leaner parrot will be more successful with heat tolerances than an overweight or obese parrot as well. With a leaner body mass, cooler moving air can cool thinner frames easier and a leaner body mass puts less stress on a respiratory system for temperature control. Conversely a heavier parrot (in the high range of normal or above) tend to tolerate the colder side of the range better than a leaner counterpart. A fully feathered parrot at good body weight can modify his feathering and breathing to handle a chill.
Acclimation to extremes also plays a huge role in normalcy and a parrot's ability to handle that norm. A parrot living in colder climates with seasonal changes with wide variances and exposed to same with an outdoor aviary has the biology and physiological responses already built in and up to handle those changes. Compare this four season parrot to, say, a Floridian parrot who sees minimal temperature and seasonal fluxes. Colder temps would be a shock to our Floridian parrot's system. If you are moving to a new region with a new temperature variable, keep this in mind as you introduce your bird to their new home. Temperature changes in small doses over a length of time will make tolerating those new numbers possible.