If you plan to stay in Thailand for more then 15 days (Visa on Arrival grants you a 15 days stay), you would have to apply for a Transit or Tourist visa.
A transit visa allows you to stay in Thailand for 30 days. You can stay in Thailand for 60 days on a tourist visa. The visa application has to be made either to the VFS centers in Delhi and Chennai or the Royal Thai Consulates in Mumbai and Kolkata.

Requirements for Tourist/Transit Visa:
You can also obtain a double entry transit/tourist visa. This allows you two entries into Thailand. You can stay for a period 30 and 60 days per entry respectively.
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