What is the relationship between burning sensation of toes fingers and ischemic heart disease?

Not aware of any. "burning" is a symptom most commonly associated with a nerve. Carpal and tarsal tunnel (nerve compression), neuritis (inflammation) and some metabolic diseases (like diabetes and anemia) can also produce a burning feeling. The most i can think of is angina can sometimes cause the left arm and fingers to tingle or even burn. It certainly would have no affect on the toes, though.