What happens when reaching the max temperature on a temperature sensor?
Thanks to 0x6d64 for pointing out the C/F discrepancy.

The data sheet says:


  Rated for full −50° to +300°F range


In C that is -45°C to 148°C - not enough for your needs.

Your main problem at that kind of temperature is going to be the melting of the solder you're using to attach the LM34CZ.

Personally I'd use a thermocouple.  Rated an hundreds of degrees (usually 400+), they allow you to keep all sensitive circuitry away from the hot area.

You'll need a converter chip to allow you to reliably use a thermocouple of course.  Most people use the MAX6675, but that is being phased out to be replaced by the MAX31855.

Both are surface mount, so you'll need to etch a PCB to mount it on, or get a breakout board (8 pin SOIC).

Both the chips are pin compatible with each other, and provide an SPI interface the Arduino can talk to easily.

I have had a MAX6675 working on my Arduino, and am waiting for some MAX31855's to arrive so I can check to see if my Thermocouple Library for the Arduino works with them.