I want a number for fiction purposes.
* We are imagining that the ball will be "thrown" by magic, not by some existing technology or real-world process that has built-in limitations. It's just gonna go zoom!
* We will go from room temp (defined here 22 Celsius / 72 Fahrenheit) to "temperature X" in the space of 60 feet, 6 inches (or a reasonably close estimated distance). This is the distance from a baseball mound (actually, the rubber) to the front edge of home plate.
* The event will occur at sea level, at 22 Celsius / 72 Fahrenheit. But for our imaginary purposes, humidity or other atmospheric effects should be ignored.
* By "catch fire," I mean, the surface of the ball is raised to the temperature at which leather is generally known to ignite, which according to this page,
is 212 Celsius / 413 Fahrenheit. For our imaginary purposes, we'll assume there is sufficient oxygen for the ball to spontaneously "catch fire" at this temperature.
Have at it, physics nerds!