Yes, 97.7°F (36.5°C) is within the normal range for body temperature.
The normal core temperature is not a single fixed value. Measurements across healthy individuals show a range of less than 97°F (36°C) to greater than 99.5°F (37.5°C), with the average typically cited as 98.0–98.6°F orally and about 1°F higher rectally.
So 97.7°F falls comfortably within the normal range.
A few factors that naturally influence body temperature:
Time of day — lowest in early morning, highest in late afternoon/evening (circadian variation of ~1°F)
Measurement site — oral, rectal, axillary, and tympanic readings differ slightly
Activity level — strenuous exercise can push core temp to 101–104°F temporarily
Age — older adults tend to run slightly lower
The commonly cited "98.6°F (37°C)" as the normal temperature is a historical average from a 19th-century study. Modern research shows meaningful individual variation, and a reading of 97.7°F is entirely normal.
— Guyton and Hall Textbook of Medical Physiology, p. 892
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