According to my family's notes there was also a Thomas born in 1844 in Clare Abbey, County Clare, Ireland (whom I forgot to mention)
There might have been twins Michael and Thomas (1839) - it's possible that this Thomas died and the next child was named after him.
Thomas (1844) apparently spelt his name HEHIR - like your ancestor.
Within the family the spelling varied e.g. O'Hare, O'Hehier, O'Heir, Hare, Hair etc.
It is believed that Thomas went to America.
Hope we can be of some help to each other.
Just a note - the subject header for my previous message should have read Killaloe, County Clare