The second study found that woollen pyjamas had an even bigger impact on older adults aged 65 to 70.
They fell asleep after 12 minutes compared with 22 and 27 minutes for those wearing polyester or cotton.
Researcher Dr Paul Swan, from the University of Sydney, said: "Not so long ago sleeping under wool bedding was the norm, and science is now rediscovering the benefits of sleeping in wool.
"Maybe it is not a coincidence because wool regulates your body temperature far better, keeping you in what is known as 'the thermal comfort zone'. You therefore not only fall asleep quicker, sleep longer, but also have deeper, better quality sleep.
"Enjoying good sleep has become increasingly difficult in modern times, and so anything that helps is great for your mental and physical health."
The research was carried out in Australia over periods of nine and four nights and involved 17 students and 36 older adults.
Participants were put to bed in British-level night-time temperatures of 17C (62.6F).
Figures from the British National Psychiatric Morbidity Survey indicate that as many as four in ten people in England suffer from some form of sleep disruption or insomnia.
The proportion has been steadily rising over the last 15 years, due in part to the increasing use of screens emitting blue light, which triggers production of melatonin and serotonin, the hormones that control wakefulness.
Another report conducted by the Sleep Council found that the proportion of people who said that they "sleep very well most nights" fell from 25 per cent in 2013 to 17 per cent in 2017.
Having the bedroom at the wrong temperature is also thought to play a role in sleep disruption.
Experts recommend that a room temperature of just over 18C.
Sleep onset is normally initiated by a decrease in core body temperature and an increase in skin temperature.
Core body temperature continues to decrease until it reaches a stable lowpoint, rising as a person wakes up.
Previous studies have found that a cold bedroom is particularly associated with rapid eye movement, where the activity of the brain is quite similar to that during waking hours.
Findings from the first new study, reported in the journal Nature And Science Of Sleep, were released to mark Wool Week, part of the Campaign for Wool whose patron is the Prince of Wales.
The second study, funded by the wool industry body Australian Wool Innovation, has not yet been published.
