Bad idea as most drones only have a battery life ranging between 8 and 20 minutes.
I realize that what I'm about to offer is out of most people's lanes but you will find it effective and fairly inexpensive. As I've been working with drones, video surveillance, and shooting for a long time there are some things that overlap between them. A cheap, home made video transmitter and receiver functions well out to several miles. All that's required is a little easy to assemble and set up equipment and a clear line of sight. If you're shooting that far you already have the clear line of sight. It's totally legal as the system will operate on 900MhZ.
A quick trip to FPV drone websites (ex: GetFV.com) will reveal a bunch of sources for very, very small 12v video cameras. Linked with an inexpensive video transmitter they can broadcast to what's known as a "diversity monitor" miles away. The monitors contain their own video receivers and battery power supplies. The typical monitor size is 7" diagonal but 10" are available through various sources. 10" is a lot better. Most also have the ability to record video onto an SD card. The monitor internal power supplies typically last about an hour. An, 11.1v (3s), 1200mA lithium polymer battery will power a small video camera for over an hour. Spare batteries are very cheap to obtain and their diminutive size makes having a couple spares pretty convenient. Making up a battery adapter plug let's us use the same batteries employed for the video transmitters as external back up batteries for the monitors. You can shoot all day and review every shot without moving from your perch.
So a tiny video camera, video transmitter, diversity monitor, a few batteries, and two cheap tripods (one for camera, one for monitor) can replace expensive spotting scopes, web based services, binocs, and overcomes the heat shimmer. Total cost runs between $200-$300.00. A little fingertip web shopping can do it for less. The monitor will be the most expensive component. Just don't shoot the camera. If you get a wild hare you can shoot the batteries and watch them explode but make sure there's nothing flammable around.