January in Monroe is the coldest month of the year. In January, the weather in Monroe is typically warm. Average daily high temperature in January is about 11 degrees above zero. On average, Monroe has 12 partly cloudy, 11 sunny, 7 rainy, and 1 cloudy day in January. The rains are usually heavy. January as well as February, July, August, and December is considered the most uncomfortable time to visit Monroe.