Sending Temp. Readings from one Arduino to another Arduino

I appreciate that you already have the Ethernet shields but the simplest way to communicate between the two Arduinos is to use a Serial link. No extra hardware required. SD card reader boards are very cheap if you want to log the data.

Sending the data simply involves printing it to a serial interface, probably using SoftwareSerial to leave the hardware serial port free for debugging.

Have a look at Serial input basics - updated for examples of how to receive and parse the data.