The Med area will not quite as warm as you are used too at the end of January.
Given the weather conditions there will not be much available anyway for the eastern end.
Malta/Portugal will not be lying on the beach weather.
If you want warmth and sun best you can do this time of year is the Canaries. I booked one in Lanzarote for February only yesterday.
Work out a cheap flight Ryanair/Flybe/Easyjet/Others from the regional airport of your choice to a destination.
Once you have that and your dates then go to Alpharooms and look for some accommodation in your desired resort for the same dates.
http://www.alpharooms.com/Only use Tripadvisor/Expedia for checking customer reviews on your chosen accommodations and resort advice. These are still online travel agents and charge commission to accommodation providers who load their prices. Alpharooms is the same but is the cheapest in the market.
When checking the reviews be aware that the fact there are some bad does not make the place a bad one. There will always be some people who expect the earth for little and will post negatively when their expectations are not met.
I have stayed in a fewf places on a couple of occasions slated by the reviews on Tripadvisor but found them comfortable and ok. If there are some good/some bad then it is probably ok.
So once you have the accommodation you want book it. then go straight back in and book the flights. Part of your research should include how far is the resort from the airport as you will need to arrange your own transfer. Alpharooms will offer you a car (at cost) as part of the booking process anyway (collect/dropoff) at airport. Quite reasonable model for around £90.00 for the week.
I use this method usually at least twice a year.
Apart from when I go on cruise ships I always book my breaks like this even to the USA/Canada although I will tend to use Expedia for choosing accommodation over the pond (but still checking the reviews on tripadvisor) More often than not having sussed out a place on Expedia I will try and book through their own website or even phone them with a card number. Again this can lead to a significant saving.
Many people whinge and moan about airlines like Ryanair but I see them as a means to an end, simply a bus. I do not eat/drink on their planes, play by their rules in that I only take cabin luggage to the prescribed sizes and have no trouble.