2001 Toyota Echo car problem

Engine Cooling problem
2001 Toyota Echo 4 cyl Two Wheel Drive Manual

I have a problem that occurs intermittently, and therefore would be difficult for a mechanic to necessarily find. Sometimes, when my car is started "cold, " the car will lose power when I put my foot on the accelerator after I brake for the first time. I live at the top of a small hill. There's a stop at the bottom, then I turn right to head out. That's where the power loss occurs from time to time. The car doesn't stall, but I put the accelerator further and further down, and then after a three-second hesitation, the cars gets power back and everything is fine (and it doesn't do it again the rest of the trip).
. What could it be an indication of? Is it
related to the engine, transmission, brakes, or what? I'm stumped. All these happens only when the engine is cold but when the engines warms up the problem is gone.