Home Energy Affordability Tax Relief Act of 2014 or the HEATR Act of 2014 - Amends the Internal Revenue Code to allow an individual taxpayer an income-based refundable tax credit for energy costs for the taxpayer's principal residence. Limits such credit to the lesser of 33% of such costs or $500. Allow such credit for residential energy costs paid or incurred after the enactment of this Act and before April 1, 2016.