Warm vacation for December-January

What do you consider warm?
From one based in Chicago I would consider Andalucia, Spain or Sicily, Southern Italy, Greece.
But it is chilly at night.

Chilly at night is okay. Warm would be over 65 F. Sunny would be very good too!

Canary Islands for winter warmth and sunshine

None of mainland Europe will be that temperature in December/January. There are places such as southern Portugal or Cyprus when you may get the occasional day that hits that temperature, but you would be very lucky if you had this for an entire week.

The Canaries would be your best option, although this is primarily a winter sun/ beach destination. I have been on Fuerteventura for over 3 weeks now and have only managed 6 days on the beach so far, as the weather has been too cold/wet/windy, some days only half your target temperature, albeit such a prolonged spell of bad weather is unusual, I understand. There isn't much to do here when the weather is so bad.

Head to the Caribbean or further south if temperature is important to you.

65F (18C) is quite a high standard if you mean you'd like the daily high temperature not to dip below that. Seville, Spain, is probably one of the hottest places in Europe at that time of year, and its average high temperatures for December and January as shown on Wikipedia (which admittedly do not include recent years) are just a tiny bit below 65F, which means there were many days when it didn't get that warm.

If you want to check actual, day-by-day temperatures for some possible destinations, go to wunderground.com, enter your destination, choose History, choose Monthly, and select December 2017. Go back several years. Then do the same with January. A lot of weather data sources only give you monthly averages, and averages hide extremes.

Seville has been lower than your ideal temperature every day for the last week, which wouldn't be much different to January.

Southern Sicily - Syracuse, Ragusa, and maybe Catania all could be upper 50's low 60's that time of year. And depending on how long you have you could fly from Catania to Valletta, Malta which may be a bit warmer and is an interesting place. It all depends on how long you have and what your interests are. Most of mainland Europe will be a bit cooler than the islands.

Not in Europe of course, but consider

A cruise around the Horn of South America.
A trip to New Zealand or Australia.

Does it have to be the European continent in winter? The Canaries are Spanish, Madeira is Portugese both warm in winter in the Atlantic, while Guadeloupe and Martinique are Caribbean French departments. St. Martin/San Maarten, under reconstruction after Irma, is part of France and Netherlands. In any of these you'll see EU projects underway and use the euro. Otherwise, southern tip of Spain is warmer than the rest at that time of year.

Thanks for all the great ideas. Will consider other places than Europe, and maybe Southern Spain. This has been very helpful.

We loved Siracusa (Ortygia) when visiting in one year in late spring. My husband asked some restaurant owners: "What's the weather like here in January?" They replied, "A lot of rain." We experienced a lot of cold and rain in western Sicily one year in mid to late March - and also some nice hot, sunny weather a week further on in Agrigento. Anymore, I'm not sure there's much predicting; someone else alluded to that.

Hawai'i is always warm, fun and interesting -- used to visit every year for Mele Kalikimaka.