And no, there's 2 * 2 pins that are labeled GND and Heat sink.As Grumpy_Mike explained a custom PCB can be made to act as heat sink (within limits).A vero board can not, because it has no large piece of copper, just a lot of very small pieces.Therefore a vero board will do a very poor job at this.
These 4 pins are both GND and heat sink, not either one.Use all 4 to have a more efficient path to get rid of heat.Buzzer that makes you turn it off ?Why not have the Arduino handle this by taking action in case of overheating, it's available right there.
Are those sidepods functional ?Very unlikely.If the body is metal, you can use that for heat dissipation.But if you connect it directly, then you have GND on the body of your car and need to remind that.
Do you read datasheets ?...Directly next to that on the left side, the datasheet tells you the device can handle 600 mA.Earlier you were asking about H bridge drivers for over 1 A....
It is very hard to help OP because of all of this, and i really tried.