Regulator circuit design
I have drawn your circuit in LTSpice and could not get it to work at all.

I replaced Q1 and R1 with a voltage source and a simulation DC sweep.
Your first OP07 stage has no supply, I added that but the OP model seem flawed. I replaced it with a LTC7652 provided in LTSpice. 

I don't understand the point of R2 (please enlighten me!) so I removed that.

I'm not totally familiar with the concept of pn-junction measurement but for this application I guess all you want is a trip point where the peltier starts.
The trip point on U3 (second OP stage) seem to be set by the potentiometer to almost 5V. To reach that voltage the input voltage of 0.62V needs to amplified about x8. But the first stage is set to amplify 1+825/1 = x826. I replaced R4 to 8k. 



I'm sure you want to modify this a bit, but the simulation seems to run fine. BTW the body diode of the MOSFET in your hand drawn schematic is drawn in the wrong direction.

The PWM solution would work in combination with the above circuit if you attach pin 4 (reset) to the output of the second OP (comparator). However, you must adjust the voltages from the comparator so the 555 circuit doesn't get fried. Check the datasheet of the 555 chip you use and divide the output from the OP accordingly. The 555 can then drive the NMOS directly from its output.

I'm not giving any hint on if you should use PWM or not for Peltziers since I find the information inconclusive. Olin has a point in the other Peltzier question on the forum, that mechanical stress might destroy the element over time.