I made a test with a DHT22 inside a dark box, uploading data every 15sec to thingspeak. Distance between DHT22 and ESP-01 was 4cm.
I tried powering the DHT22 from 3,3V output from AMS1113 with a 470uF cap. All the readings were very inaccurate, with +/- 2ºC temp and +/- up to 5% hum:
My next try was powering the DHT22 with 5V, using a simple resistor divider to communicate with the ESP-01. Data was really stable, with +/- 0,2ºC temp and +/- 1,5% hum:
Hope this helps.