If you can take that object's temperature loss in terms of radiation just as a black-body, you can have your answer in wikipedia easily.
In equilibrium, for each frequency the total intensity of radiation that is emitted and reflected from a body (that is, the net amount of radiation leaving its surface, called the spectral radiance) is determined solely by the equilibrium temperature, and does not depend upon the shape, material or structure of the body. For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is due entirely to emission. Here, you take total output by ball minus total input by surrounding.
(so the temperatures of ball and environment are important with the surface area of ball)
Ofcourse friction is important that how fast that object is relevant. That was already asked and answered below link.
(area of ball, material of ball, material of surrounding, speed of ball, structure of ball(flat surface or noisy surface))
After what speed air friction starts to heat up an object?
I want to add some more parameters, electric charge of object and magnetic field of the surrounding. When you move a charged object in a magnetic field that is not parallel to velocity of object, object is under a force. If it is fast enough and is in a constrained orbit, it will get hotter because electric charge on it will get affected and move to one side of object thus making the object to have a voltage-potential between two poles. When charges move to these poles, it has conduct a curent that heated it. If you change direction of flight of obejct, opposite polarisation happens and heats more. So even discontinuity of velocity is important if there are parameters such as charge and magnetic field.
Lets take bigger objects like planets. When two objects move close, they strain each other with gravity and get hotter. Especially the closermost parts.
Lets take smaller object, they are so small that even time is a parameter. You dont even need to move that. There is always a possibility of a molecule to change its state, angle of bond, direction of bond, polarisation (like inversion of NH3) which makes them resonate with a power source which could be even the infrared-band . If you take a small group of these, their natural-state-changing becomes more important thanks as Quantum-Physics shows.
Again for small objects, if those are fast enough(coming near speed of light), their mass increase and make the time go slower so the expected temperature would be smaller or I am wrong.
As Nathaniel reminds, heat change with conduction become more important as the heat transfer constant of surfece between ball and surrounding material increases(fluid density can be important too), surface area of ball is also important. When fluid passes faster, it takes heat faster. Pressure of surrounding fluid on the surface can be important too(maybe multiplies the transfer constant)
After speed of sound, some phasechanging can occur near surface and that could affect heat conduction too.