GREENVILLE, S.C. (FOX Carolina) – Near record warmth comes Tuesday ahead of more unsettled weather toward middle and late week. The warmth sticks around through the week with record highs in jeopardy both Tuesday and Thursday for Greenville and Asheville. In Greenville, a nearly 100 year old record could fall Tuesday. The record to beat is 76 degrees set back in 1927. In Asheville, a 135 year old record could fall. The record to beat there is 73 degrees…