I have a feeling you're gonna enjoy this trip !
There are direct flights, trains and buses for this journey. Catching a direct flight is the fastest way to do this journey. Direct trains are available as well. Also direct buses are available. Hyderabad (Andhra Pradesh) to Coimbatore (Tamil Nadu) distance is 932 km and you can get there by flight in just over 1 hour and 10 minutes. Going by train won't be that fast but you will get fares starting from ₹ 401.
It's gonna be warm and sunny, and did I mention warm ?