Tenerife tis usually 'reasonably warm' but not 'hot' in January:
http://www.holiday-weather.com/tenerife/averages/january/
However it does have a reputation for often being very windy during the winter months.
As stated in that link, it can be march warmer in the south of the island at that time of the year than in the north.
The Canary Islands are by far the most popular destination for British holidaymakers in the winter, simply because it's the only place to go that's far enough south to get some warmth without being expensive (as, say, South Africa - or even Australia - might be) or troubled by terrorism (as many north African countries can sometimes be). So, while Tenerife won't be as busy as in the summer months, it certainly won't be devoid of life either.