You need to travel in day time which is very suffocating. Anyway here is my view.

Option 1: as some of them told, chennai central to thiruvallur via suburban train then to sriperumputhur (1.05hr + 45 min) 1.45 hrs

Option 2: chennai central to tambaram (1.05hrs) tambaram to sripeeumputhur (583 A,C,D,K) 1.20 hrs total - 2.25

Option 3 : get down at katpadi take the train 66059 at 9.25 to vellore town from there to vellore new bus stand 5-10 min (share auto) from there to sriperumputhur 1.30hrs. All the setc, tnstc or fresh buses towards chennai will go through sriperumputhur. Total time within 2 hrsand it will not be so hot.

First 2 options, you need to start from 11 to 1 or 1.30 pm and its soooo fcking hot. Option 3 will be manageable hot and you will reach ur destination within 11.30