The last couple of days has seen cold morning in Chennai with yesterday recording the lowest temperature of the season in both the City & Airport observatory. This trend of cold mornings is expected to continue for the next few days as well with most parts of Peninsular India enjoying a mild cold wave.
A few factors working together has meant this cold wave type conditions have set it over Peninsular India though it has set in delayed for this year. 
The first most important factor is the presence of High Pressure over Peninsular India, as one could observe from the chart above, the region to the NW of Chennai sees high pressure setting in which is the primary driving factor for the cold wave type conditions in most parts of South India.
The clear skies with pretty much very little clouding means during day times though it is slightly warmer than normal the ground heat gets radiated back into the atmosphere allowing the nights to be cool. In what is likely to be one of the best periods of winter for most places in South India, except for West Coast, the day is likely to be moderate and may be slightly warm in a few places of South TN.
Across the Peninsula Night time is expected to be cool with only a very narrow band of coastal places in TN & Kerala being moderated by the presence of seas close by resulting in temperatures above 20°C. Most interior places of TN & South Karnataka are expected to see night time temperatures around 15°C. The Lambasingi region of Andhra Pradesh near Vishakapatnam, known as the Kashmir of Andhra, could possibly see sub 5°C at most places.
Chennai Weather Update: Warm day with cloudy skies in the morning and fairly clear skies later in the day for Chennai. Day time temperatures expected to stay around 30°C. Clearing skies in the afternoon could bring to cool evening and set up cold morning in Chennai. Expect another cold morning in Chennai tomorrow as well with the minimum temperatures expected to stay around 20°C