Just FYI, sharing information.
I am using ESP8266-12E nodemcu dev kit with DHT22 and deepsleep (sleep 5 minutes, measure temp and humidity, sleep 5 minutes, …)
This is how the board exactly looks like:
When I measure current it was 75mA when wake up and around 2,5mA when in deepsleep. It is powered by 4 AA rechargable NiMH batteries (4x 1,25V = 5V). I also expected lower current consumption when in deepsleep, but for now I can live with it.