I am trying to terminate the unused unity-gain unstable op-amp. I have tried to terminate it with the typical unity-gain stable configuration (http://www.maximintegrated.com/en/app-notes/index.mvp/id/1957) and so far in the lab, it seemed to work and gave stable output. However, I am still concerned about it as it is unstable at unity-gain region mentioned in datasheet. I want to learn if there is anything more robust than using unity-gain termination configuration. The amplifier I am using is OPA2614 from TI. So far I have tried this to stabilize the output at 12V but don't know if this is the best way.: 
Electronic – Terminating unused unity-gain Unstable op-amp
operational-amplifierterminationunity-gain
Related Solutions
I presume that your 12V is also supplying the E-P transducer power (and perhaps other stuff) and that's why the regulator is getting hot. You should heat sink it so that the case temperature is reasonable if you want reliable operation, or use a switching regulator. The exact numbers depend on your ambient range and desired reliability, but "wicked hot" sounds like it exceeds the 60-70°C range that I'd like to see for general purpose applications.
The 'fluctuation' in op-amp output could be caused by oscillations. The LM324 is fairly robust with small capacitive loads (such as could be caused by cable to the transducer), especially for gain > 1, but you may still be having problems. I suggest this kind of output circuit:
simulate this circuit – Schematic created using CircuitLab
The input filter R4/C2 keeps high frequencies out of the input and matches the impedances looking out of the op-amp inputs so as to minimize the effect of the relatively large bias current on the LM324. The resistor R1 isolates the capacitive loading on the output from the internal output impedance of the op-amp. C1 forms a tight loop for AC to stabilize the op-amp. The feedback (R2/R3) is taken directly from the output so that R1 does not affect the output voltage when sourcing current (note that when sinking current the op-amp cannot get close to the negative rail when sinking more than 50uA or so, so the 0V output can't be approached even without R1). In most cases, the input of your transducer looks like a resistor to 0V so it's not an issue.
D1 and D2 conduct any transients to the power supply, saving U1 from damage due to ESD. R4/C2 and D1/D2 are optional as far as your immediate problem goes, R1 and C1 do the work. I strongly suggest you get that regulator temperature under control as well.
You are powering your LM358 from a 5V power rail: -
- It only has a 5V power rail
- Input common mode range is from 0V to Vcc-1.5 i.e. 0V to 3.5V
- Your input is 12V *10/32 = 3.75 volts
- Output range is about 0V to Vcc-2V i.e. 0V to 3V
Read the data sheet and don't expect miracles.
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Best Answer
This would be better (output left open):
simulate this circuit – Schematic created using CircuitLab
Both inputs are within the common-mode range of the amplifer- see the datasheet which gives the values with a +/-6V supply and translate by adding 6V to the numbers.