If the part is preheated, the grains will be larger because of slower solidification. The HAZ would also have bigger grains because of being in the grain growth temperature region longer. If the 316 is being used for creep resistance, this should not matter. If it needs to be tough at lower temperatures, it could be detrimental. However, if you keep 316 hot for a long time, you will also get sensitization. If this is for a high temperature (oxidation resisting) application, it may not matter, but it will if you need corrosion resistance where a chromium oxide layer on the surface is essential (in most applications it is).