Have you tried checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64) for Thomas or his relatives? The Tithe Applotment Books (1823-38): Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.
Do you know much about his emigration? Dates, the reason why he left, who he may have travelled with etc.? Generally more information was given at the port of arrival rather than the port of departure. If you knew which city they arrived at (e.g. Liverpool, New York etc...), this could be a good place to find more information, and perhaps even find out an exact place of origin.
For further assistance you might consider contacting:
Irish World Family History Services,
Family History Suite,
51 Dungannon Road,
Tel/Fax: +44 (0)28 8774 6065