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Why not just use a LM35 to feed back a voltage to a LM317 to maintain a steady temperature. Use an Opamp to get the exact amplification if required to set the correct temperature if the voltages are too small.
Basically, the LM35 is 10mv per deg. So say you want it at 20 deg = 200mV.
You can feed this value back into the LM317 via a pot for setting your desired Temp. This way your temp stays stable, if the temp varies, the current will either increase or decrease to compensate. Plus its slow DC, so no noise.
This is similar to a design i made for a turbo boost controller about 10 years ago to control boost if temperature increased over a set position.
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