follow up to hot water tank use on Shabbat

Question

Please clarify for me: I was always under the impression that using hot water on Shabbat was a problem because the hot water tank would refill with cold water. At that point the pilot on the bottom would engage and heat up the new cold water to reach the setting on the dial. I noticed a response you had about 125 degrees, If the setting is below 125 degrees this is not an issue. Did I understand that correctly. If the dial is below 125 degrees is it ok to use hot water on Shabbat? Again, was my statement earlier about refilling the tank and the tank getting reheated a non issue if the setting is below 125 degrees. Thank you as always.