Landsat 8 data could be used to calculate the Land Surface Temperature, but I do not think the Landsat 8 can provide a night temperature. However, you can use the MODIS LST (Terra and Aqua) to measure the day and night temperature for New Delhi and any other area within the world.
You can calculate the land Surface temperature but you must know the counting values of the thermal bands un metadata and apply equations, first calculate Top Atmospheric (TOA) after convert to brightness temperature, calculate NDVI, vegetation ratio, emissivity and finally the LST