Nice ! Looks like you're all set for your vacation ?
There are direct trains and buses but no direct flights for this journey. Hyderabad (Andhra Pradesh) to Shirdi (Maharashtra) distance is 594 km and you can get there by flight + cab in just over 7 hours and 50 minutes or by train fares starting from ₹ 337.
The heat there will make you sweat, but it's surely bearable.