Tirunelveli is hot for most of the year. The most comfortable months for sightseeing are November through February, when temperatures drop to a comfortable 20–30°C and the air is dry. March through May are oppressively hot, with highs above 38°C and dusty winds blowing off the eastern plains.
The two monsoons matter. The southwest monsoon (June–August) brings rain mainly to the Western Ghats and is the best time to visit Courtallam, when the falls are in full flow. The northeast monsoon (October–December) is when Tirunelveli town itself gets most of its rain — short heavy downpours that can briefly flood the lower streets but rarely disrupt travel for long.
The big festivals at Nellaiappar Temple are the Aippasi Brahmotsavam (October–November) and Vaikasi Visakam (May–June), both worth timing a visit around for the temple processions.