Sleep onset isn't just a matter of feeling tired — it's a thermoregulatory event. In the hour or two before you fall asleep, blood vessels in your hands and feet dilate, a process called distal vasodilation, and heat that's been stored in your core gets carried out to your skin and released into the room.
This is where room temperature comes in. If the air around you is too warm, your body can't shed heat efficiently through your skin, so the core-temperature drop that sleep depends on gets stalled or blunted. Based on this mechanism, sleep researchers generally recommend keeping bedrooms in the 60–67°F (15.5–19.5°C) range.
That range is a starting point, not a rule. Older adults tend to produce and retain less body heat, so some sleep better modestly warmer. What actually matters is whether your setup lets that hand-and-foot warming happen.
Further reading: The Best Temperature for Sleep (Sleep Foundation).