I put a partially frozen (inside) chicken in my convection oven, set it to what I thought was 400ºF (200ºC) and left the room with a timer on. An hour later it was discovered the temperature was only 150-200ºF (65-93ºC). It was in the convection oven an hour! I quickly set the correct temperature and finished cooking it. I just don't know if the hour it spent in the convection oven on the lower temperature did something with bacteria. I cooked it to an internal temperature of 180ºF (80ºC) degrees. Is it safe to eat this chicken?
Assuming you thawed the chicken (to the extent that you did) in the refrigerator, and further assuming that it took less than an hour to reach a safe internal temperature, I would say you are fine. An internal temperature of 180ºF (80ºC) is safe by quite a margin.
The USDA recommends that home cooks do not keep food within the "Danger Zone" of 40-140ºF (4-60ºC) for more than 2 hours. This includes preparation and cooking time. If you thawed the bird on the kitchen counter, or if your chicken accompanied you on a long journey from the supermarket in an unfrozen state, you'll have to factor that time in.
As @Jefromi's comment on another answer notes, simply reaching a high enough internal temperature is not a guarantee of safety since some microbes produce toxins that are heat-stable.
No, do not eat food that has slowly passed through the danger zone.
In my food handler classes I learned that any food that quickly moves from HOT --> Cold is safe, and visa versa. However, it is un-safe to eat food that has slowly moved through the temperature zones.
IMO eat at your own risk.
edit for corrections