Even the southernmost places in Europe aren't 'hot' at that time of the year. 'Warm' possibly, but not definitely not 'hot'.
For example, temperatures in Southern Spain and Gibraltar are only around 16-17C. You'll find roughly similar temperatures in Southern Italy, Sicily, Southern Greece and Malta. Going west, towards Asia, doesn't help: Cyprus is only around 14-15C at that time of year.
You really need to head further south, which (at reasonable prices) means North Africa or the islands off the north African coast. Your only really cheap option here will be the Canaries, where temperatures will typically peak each day around 21C. (The only problem is that the Canary Islands are often battered by strong winds during January and February). Otherwise, you might find some bargains to Morocco. Even so, you still won't find really hot weather. (In Marrakech temperatures will typically peak at around 18-19C each day). Madeira also has daily peak temperatures around 19C but, like the Canaries, you might find some strong winds.
Weather data for this post has been derived from
http://uk.weather.com
Chris