Can the DHT11 give reasonable readings? I bought a batch of ESP8266-01 and DHT11 on ebay.

The sensors give data, but the datasheet say +/- 2 degrees. Who can live with that? Well, they claim the repeatability is 0.2 degrees, so I guess they could be calibrated.

But thet are not stable. They start a few degrees over room temperature, but gradually the reading is up to 33 degrees, more than 10 degrees too high.

Could it be the proximity of the ESP8266 giving off heat? Or are the sensors themselves heating up when reading at one read every two seconds?
It could be the ESP8266, try physically separating the DHT11, but I'm guessing that that will only help slightly.

Do you have some way of reliably calibrating the sensors? If not, then even if you are getting consistent readings, you'll have a hard time knowing how accurate your readings are.

While they're typically more expensive, it might be prudent to buy an infrared temperature sensor. If you have the budget, replacing the DHT11s with IR temperature sensors might just be a better solution, I saw that Sparkfun's MLX90614 was accurate within +/- 0.5 degrees Celsius. If you don't have the budget to replace your DHT11s, or don't want to be wasteful, perhaps you just buy one IR temperature sensor to use as a sanity check. These should be more reliable than DHT11s and you could even write a sketch to calibrate them based on the IR temperature sensor's readings.