2 Arduinos on a single 1Wire microlan?

The design uses DS18B20s (non-parasitic) to monitor temperatures at various points, and energises a couple of pump relays to distribute heating water appropriately. The data is displayed on LCD, Serial, a simple web page and logged on the Ethernet Shield's SD Card.

Sounds like a nice application.

Although the sketch is within size limits, it seems that SRAM gets filled up a

You can post the sketch so we can help optimize the sketches size?

Another option is to use a second Arduino and divide tasks
Arduino 1 does sensor reading and relay control and forwards its states to arduino 2
Arduino 2 does the presentation part webserver/lcd etc.