It's the compressor that draws so much when it starts.
So if you left the freezer plugged in, the compressor would run until the freezer froze. The built in thermostat would then cut power to the compressor. It would then start and stop the compressor as needed to keep it cold; you get that transient draw EVERY time it calls for cooling.
The temp controller doesn't really do anything different, except it cuts power to the entire freezer, not just the compressor. and since you're overriding the thermostat to a higher temperature, it should call for the compressor less often and therefore make it cheaper to operate.
One variable is how tightly you try to control the temperature. if you're trying to keep within half a degree, then you're going to cycle that compressor more often and for shorter periods; basically a worst-case for cost and wear-and-tear on the compressor. If you're happy letting the temp swing by 5 degrees you'll cus the cost and extend the the life.