According to 1910 US Federal Census, brother James migrated to the USA in 1862. The whole Heffernan family probably migrated at the same time.
Sources
Clonoulty parish baptism register, National Library of Ireland;
New York State Census, 1875 - resident of De Ruyter, Madison, New York (Thomas 26, Margaret 26, Daniel 3, Patrick 2, Nellie 0);
US Federal Census 1880 - resident of Fabius, Onondaga, New York, USA (Maggie 33 (widowed), Patrick 7, Nellie 5, Thomas 6 months). The child, Daniel, had evidently died between 1875 and 1880, as had his father.
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DNA Connections
It may be possible to confirm family relationships with Thomas by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Thomas: