The Elk zones are designed to supply current, specifically 13+V through a 2.2K ohm resistor, to open/close contacts and/or attached resistance. The zones measure the resultant voltage across the zone and convert the voltage measurement to a digital value 0-255.
The principal challenge you face when connecting active elements to a zone is this supplied zone voltage. You need a low-impedance voltage source as a start, then you have to deal with the problem (usually) of non-linear behavior, and if you want to take advantage of the full 256-step range, you need to scale the output of your interface to the full zone voltage range (14V measured, according to Spanky). So your task is to to design an interface particular to the specifications of the device you are attaching, with these output characteristics.
Alternatively, you can cut the pull-up resistor for the zone, which is risky and has warranty implications, but which then simplifies the interfacing problem to one of voltage scaling.
Once you have a nice functioning linear full-scale zone input, you have to convert the 0-255 digital value to something useful, like actual temperature, humidity, pressure, distance, whatever. Let's just say that the Elk does not excel at math.
The Elk temperature sensors actually do not even use the analog zone characteristics, they use a serial protocol (again according to Spanky) which is implemented only on the main board zones 1-16. You *could* in principle design an interface for the LM34 which would implement this protocol, and then use zone definition 33 as intended. But you would simply exchange the above complexity for complexity of a different kind.
BSR and others have done considerable investigation of this situation over 2-3 years, including not incidentally analog interfacing the LM34, with mixed results. For my part, time is too valuable and there are plentiful alternatives. I use other devices for analog measurements, and use the M1 in those many situations where it functions best.