Heshko started to train at the age of 14. From an early age he had played football and handball, but eventually focused solely on athletics. He achieved his studies at the Teacher's Training College: Kamenets-Podolskiy. A member of an Italian athletic club, he has been trained by Georgiy Mironiouk since 1992, and has five times been the champion of his country, including a bronze medal in 2003 at the World Championships (Paris/Saint-Denis) and silver in the 1500 m at the 2004 IAAF World Indoor Championships in Budapest.
At Athens 2004, Heshko finished fifth in 1500 m. He also competed in 800 meters, but failed to advance in the semi-finals. His personal best time of 3:30.33 (1500 m), accomplished during the 2004 meeting of Brussel, is also a Ukrainian national record.