Weekly Weather Report for 38548, Buffalo Valley, Tennessee. Looking at the weather in 38548, Buffalo Valley, Tennessee over the next 7 days, the maximum temperature will be 12℃ (or 54℉) on Sunday 21 st January at around 4 pm. In the same week the minimum temperature will be -14℃ (or 7℉) on Thursday 18 th January at around 1 am.