For the thermal side :
On the datasheet you should have a line telling you how many °C the part increase relative to ambient temperature for each Watt of power dissipiation. Calculate the power dissipation using the internal FET resistance, the voltage and current needed.
If the temp rise (°C) is too much, you need a heatsink or split the current with multiple FETs in parallel.
I think you can ignore the current needed by the display, it should be peanuts compared to the 15A needed by the motors