ESP8266 Community Forum

I've found the solution. It was actually already already on the forum here
In this thread, there's code that can be used to replace the contents of the library file Si7021.cpp viewtopic.php?f=32&t=8002&p=41755&hilit=si7021#p41755

The library itself van be downloaded from https://github.com/LowPowerLab/SI7021
After changing the library file, I get poper output from the basic sample:

BASIC DEMO
------------------------------------------
Heater Status = OFF
Humidity : 59.59 % Temp : 20.47 C 30
Humidity : 59.48 % Temp : 20.50 C 29
Humidity : 59.48 % Temp : 20.49 C 28
Humidity : 59.49 % Temp : 20.47 C 27
Humidity : 59.48 % Temp : 20.46 C 26
Humidity : 59.47 % Temp : 20.45 C 25
Humidity : 59.47 % Temp : 20.48 C 24
Humidity : 59.48 % Temp : 20.48 C 23
Humidity : 59.48 % Temp : 20.45 C 22
Humidity : 59.49 % Temp : 20.47 C 21
Humidity : 59.48 % Temp : 20.48 C 20

ESP 01

void setup()
{
Wire.begin(0,2);
ESP8266 -- Si7021
pin 0 pin SDA
pin 2 pin SCL

void setup()
{
Wire.begin(2,0);
ESP8266 -- Si7021
pin 2 pin SDA
pin 0 pin SCL