Is there any library for use Arduino Uno with esp8266-01 module? I have a Arduino Uno and the esp8266 module,(NOT THE SHIELD). 

I was looking for some library that I could use to connect to Wifi and set a webserver, but I can't find anything. I just found for Arduino Wifi Shield which uses SPI. 

It is possible to use arduino lets say to read a LM35 and then send that data to the ESP8266 module and serve it in a page as webserver?

I know that I can use AT commands with ESP8266 to connect to wifi and to create a server, but I cannot find any function to set the data to be served.

https://www.espressif.com/sites/default/files/documentation/4a-esp8266_at_instruction_set_en.pdf
Why involve the UNO at all.  The ESP88266 could be programmed with the Arduino IDE to read the sensor and deal with the internet all by itself.  It doesn't need the UNO to do what you want.