On the Caribbean coast, there is not a lot of seasonal change in the average rainfall and temperature. They don’t have a really dry season like the Central Valley and Guanacaste Province in the northwest. It rains some all year round, usually in the afternoon. Of course during hurricane season (July-November) tropical storms can change things real fast, and when it’s raining really hard in the Central Valley (usually September & October) the rivers can flood going toward the Caribbean, but you shouldn’t have to worry about that in January. The temperature goes up to the high 80s in the day time and high 60s at night year round, and it’s humid. If you are used to the dry heat of Arizona, you will feel a difference. I’ve been there in July and December, and it was very humid both times of year.
If you’re interested, the northwest beaches on the Pacific side have a real dry season (December-April) when rainfall and humidity drop way down. The southwest corner down around Corcovado is more like the Caribbean with more rainfall and higher humidity.
Here are some charts that show average monthly rainfall and temperature for different regions. The chart for Tortuguero refers to the northeast Caribbean coast; Putarenas is central pacific coast; Montezuma is the southern tip of the Nicoya Peninsula; and San Jose is the central valley.
http://www.explorecostarica.com/climate3.htm#SanJose