Powering Arduino and transistors with one power supply > 12V
The voltage regulator (on the Vin pin) is supposed to be provided with 12V at max, since it is not cooled (it is a linear regulator, that dissipates the excess voltage as heat). If you have significantly more, you should at best buy a little switching regulator, to directly get a regulated 5V to feed to the 5V pin of the Arduino (that's what I suggest). Be sure to use a regulator, that can provide the needed current (which also depends on what else you provide over the Arduino).

If you really don't want to use an extra regulator and you don't have much more than 12V (maybe like 15V), you might get away by cooling the voltage regulator on the Arduino. The voltage regulator on a genuine Arduino will go into emergency shutdown, if it overheats, but it will not be damaged easily. Here you could try a bit. But be careful to not stress it too much. The clones from china often have different/cheaper regulators, that will mostly be fried if you overheat them. But they are very cheap.