All of those would be present. Only an extremely small amount of heat would be transferred by radiation. However, the actual heat transfer to the lake as a whole would be the result of both convection and conduction. In most cases, we would think of the overwhelming amount of heat being moved most rapidly throughout the lake as a whole being convection- the actual physical movement/mixing of the "hot" spring water. However, the individual "hot" water molecules would also distribute their energy very rapidly to all the surrounding lower-temperature water molecules by conduction. My answer would be that for a typical spring, the heat is transferred fairly widely and rapidly throughout the lake by convection, but that same heat is also transferred throughout the lake's molecules by conduction.
