It is a pretty simple straight-forward route. Chennai - Chengalpattu - Tindivanam - Villupuram - Perambalur - Trichy on the NH 38 (old NH 45). 5+ hrs of travel by car. 300+ kms. Excellent road conditions.
Just continue on the same route on NH 38 (old NH 45). Post Trichy - Viralimalai - Melur - Madurai. Additional 2+ hrs. 150+ kms more. Road conditions remain good. Expect traffic from Samayapuram - Corporation (inside Trichy).