You can connect your "4 digit (seven segment display)" directly to the 12V with correct serial resistors.
When you will light the segment you will "sink" the current. The "sinked" current is not provided by the arduino regulator but directly by the 12v power supply. This current flow out the chip only by ground wires.
The "heat" is function of the U*I product by decreasing the current you minimize the "heat" of the régulator.
Due to my poor english an example is better :
4 digit 7 segment need 47*20mA = 560 mA
Regulator input =12V output = 5V, drop out = 12 -0.8 -5 = 6.2 V (0.8V for the serial diode, see schematic).
current for the arduino board ~ 50 mA. (it is an estimation)
- 4 digit *7 segment current furnish by arduino regulator :
Power (regulator) = 6.2 *(0,56+ 0,05) = 3.8 W
Thermal resistance of the regulateur case : 220 °C/W
Ambiant temperature : 30°C
Regulator Junction temperature = 30 + 220 * 3.8 = 866 °C >120°C -> the regulator die.
- 4 digit *7 segment current furnish by 12v power supply
Power (regulator) = 6.2 *( 0,05) = 0.31 W
Regulator Junction temperature = 30 + 220 * 0.31 = 77.5 °C < 120°C -> the regulator is alive