The temperature, 10 degrees above the seasonal norm, is the highest since records began in 1852, exceeding the previous 13.2 C (55.76 F) peak of 1929.
Berlin and the Czech Republic also registered new-year highs of 11 C (51.8 F) and 12.5 C (54.5 F), respectively.
Austrian skiing resorts have been hard hit by the unseasonally mild weather, but forcasts of up to 70 centimetres of snow in the west of the country for this week put the smile back on the faces of tourism professionals.
The lowest temperature in the Austrian capital for this time of year, - 17.6 C, was recorded in 1891.