Arduino as analog to digital converter for temperature sensor
Both the ESP8266 and the Arduino have UART serial interfaces. This is by far the simplest method of communicating between two boards.

Connect the TX of the Arduino, through a voltage divider to drop it to 3.3V, to the RX of the ESP8266. Connect the grounds together. That's all you need. Yes, you can connect the TX of the ESP8266 to the RX of the Arduino but if you are never going to send anything from the ESP8266 to the Arduino then there is little point.

Then, with both devices set to the same baud rate, you can Serial.print on the Arduino, and Serial.read on the ESP8266. Just follow one of the many many tutorials about communicating between Arduinos using UART.