Does the temperature of the heat source or the distance the heat source is from the water makes a difference?
I believe the question is in regards to making a difference in the amount of time it takes to heat the water?
Simply put, the answer would be a "yes". The amount of time it takes to heat a substance has to do with the substance's specific heat capacity. Specific heat capacity is defined as the amount if energy (in Joules) that it takes to raise the temperature of a substance by one degree Celcius. Temperature is simply a measurement of the amount of kinetic energy in a substance. Thus, higher temperatures have more kinetic energy to apply to the water. Therefore, the water's temperature will move upwards faster.
Distance also affects the amount of time it takes to heat the water. The further the heat source and the water are from one another, less energy is being transferred (some is being lost to the external environment), and the more time it will take to increase the temperature of the water.