I got one of those ESP-01s and a Ds18b20 (Dallas) sensor from Aliexpress for about 2 euros or so. The sellers say that they can get anywhere from 3.3V up to 12V. The ESP-01 works perfectly, but the temperature was always off by a number of degrees.
Given it has been working for months, I always thought that the thermometer was shit, and was looking at ways to offset it via software. But then I realized that the power supply of my breadboard was set to 5V.
I changed it to 3.3v, and this is what happened:
As soon as I changed the power to 3.3V, temperature fell immediately 4ºC. The extra degree this morning seems to by my girlfriend closing the door of the lab (which makes it colder).
In conclusion: The ESP-01 will probably work with any voltage, but don’t trust temperature readings with it (the room is around 20º, so even with 3.3V, it’s still off).