Thanks to All!
I think I was able to modify ESP-01 for deep-sleep according to that description. So, ESP device goes to sleep every 120 sec - I can see the drop of consumed current from the USB watt-meter.
I was not able to power ESP from cr2032 - the power voltage barely reached 2.8v, Am I correct that it is not enough for ESP8266? What is a typical battery power source for your deep-sleep devices?