Hello there! Welcome to the forum!
Tamil Nadu is generally a region with tropical climate all-year round. Most of the areas in Tamil Nadu fall under the tropical savanna climate. A smaller part of the region falls under the subtropical humid climate. There isn't much variation in the temperature during the year. But there are three seasons in the region.
The first one is the summer season from the months of March to June. Temperatures range between 25°C to 45°C. The hottest month is usually May and temperatures can exceed 40°C during this month. It's not the best season to visit Tamil Nadu as it can get uncomfortable especially if you're not used to the heat. The hot winds from the plains also blow this way during the months of April and May which adds to the heat factor. If you'd still like to visit Tamil Nadu during this season, opt for higher lying areas like Ooty, Kodaikanal, Yelagiri Hills and Yercaud.
From the months of July to December, these are the monsoon months of the region. It's actually divided into two parts: the Southwest monsoon from July to September and the Northeast monsoon, from October to December. The state is highly dependent on the monsoon season for its water supply. Temperatures range between 25°C to 30°C during this time. Although it rains, the climate is still humid. It's also not a good time to visit the region, unless you're going to the higher areas.
The last season is the winter, which are the months of December to February. This is the best time to visit Tamil Nadu as the weather and climate is pleasant for sightseeing, especially the numerous temples in the region. Temperatures range between 10°C to 15°C. Temperatures are lowest during the month of January. Also, the harvest festival called
Pongal is celebrated during this time. Bring your light jackets and other winter paraphernalia during this time. But if you come from a colder region, the cold during this time won't bother you.
I hope this helps.
P.S.
I'd say that the heat in Delhi and Tamil Nadu can be comparable. But Delhi temperatures during the summers can exceed 45°C, so it's a bit hotter during June. Also, July is definitely humid and hot in Delhi, despite the arrival of the monsoon season.