I would recommend to not drink only distilled water as it lacks the elecrolytes your heart needs to run smoothly.
Before Iodine, Salt, real salt was calming to my hypo T heart; I had palpitations, missed beats, deep hard pounding etc.
"Electrolytes are substances that, when placed in water, can carry an electrical charge. Electrolytes are required for almost every physiological function, such as maintaining water balance in cells, making enzymes and creating energy. Two of the most important electrolytes to cell function are potassium and sodium, according to the "Textbook of Physiology." Their relative ratios in the blood are controlled by the kidneys. Also, different cell types have their own individual control mechanisms to maintain these two electrolytes in tight relative balance. This balance is particularly important in certain tissues that depend on electrical activity to function properly. The heart is extraordinarily sensitive to electrolyte balance since its rhythm is controlled electrically. http://www.livestrong.com/article/350038-electrolytes-for-heart-palpitations/
"Distillation is the process in which water is boiled, evaporated and the vapour condensed. Distilled water is free of dissolved minerals and, because of this, has the special property of being able to actively absorb toxic substances from the body and eliminate them. Studies validate the benefits of drinking distilled water when one is seeking to cleanse or detoxify the system for short periods of time (a few weeks at a time). Fasting using distilled water can be dangerous because of the rapid loss of electrolytes (sodium, potassium, chloride) and trace minerals like magnesium, deficiencies of which can cause heart beat irregularities" http://chetday.com/saynotodistilled.htm