You know what? I have been wanting to visit Coimbatore too!
There are direct flights, trains and buses for this journey. Hyderabad (Andhra Pradesh) to Coimbatore (Tamil Nadu) distance is 727 km and you can get there by flight in just over 1 hour and 15 minutes or by train fares starting from ₹ 401.
The heat there will make you sweat, but it's surely bearable.