Electrical – A way to ‘digitalize’ a wheatstone bridge

This should get you close. By my calcs, in your range the thermistor will be going from about 1 ohm to about 6 ohms. With a 1K resistor to hold currents down to milliamps, you need a gain of about 35 to keep your max voltage at 1V. This circuit has a gain of 34 using standard 5% resistor values. You might need to change to a rail-to-rail op amp if you're going to power it with a one-sided supply.

The key to good engineering is to keep it simple. In your case, you can use something very simple to turn on/off a relay to control a heater. A psuedo code:

int temperature;
int setpoint;
int status = 0;
int pulses = 0;
int integral = 4;
int derivative = 5;
int upperTemp = 1000; //100.0C
int upperLimit = 100; //pulses per time frame
int counter = 0;

//NO PULSING
runtime //make a timer that runs and updates temperature value
{
  read temperature; 
  temperature *= 10; //still keeping in int for faster processing
  status = ((setpoint - temperature)*integral)/derivative; //EX: (800-400)*4/5 = 320
                                                           //EX: (800-780)*4/5 = 16
  status = abs(status); //get absolute value, this for for within range
                        //(800-850)*4/5 = -40 -> ABS(-40) = 40
  if(status < 16)  //from example, 16 means that value is within 2*C, you can always 
    Relay Off;     //change this value to something else (e.g: (800-795)*4/5 = 4
  else             //4 gives 0.5*C tolerance range...which is a bit tight for temp.
    Relay On;      //anyway, play around with this value;
                   //you can also change integral and derivative if you wish.        
}

//WITH PULSING
runtime //make a timer that runs and updates temperature value...lets say every second
{
  read temperature; //every second
  temperature *= 10; //multiply by 10 for decimal place, but still keeping in integer
  pulses = map(temperature, upperTemp, 0, 0, upperLimit); //when temperature increases, 
                                                          //pulses decreases...vice versa
  //take this value of pulses to update the timer interval
  //timer's interval = pulses per second or minute
}

timer
{
  if(Relay On)
    Relay Off;
  else
    Relay On;   
}

//borrowed from arduino
long map(long x, long in_min, long in_max, long out_min, long out_max)
{
  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}

//PWM method: still need the runtime with pulsing from above. Let's say you get 75 pulses, this means that the relay will be on for 75% of the duration of each pulse and off for the other 25%. Let's say that you want to have a frequency of 1s (1000mS). Relay will be on for 750mS and off for 250mS. If the temperature is very far away from setpoint, then it might even be on for 100% of the time.

//choose entire duration by tick_interval*percentage: 100mS*100 = 10000mS or 10seconds. Back to example. If you have 75 pulses, then relay will be on for 7.5 seconds and off for 2.5 seconds.

timer //example 100mS per tick
{
  if(counter > 100) //has reached the end of time period
    counter = 0;
  if(counter > pulses) //pulses from above is now the duty cycle
  {
    if(Relay is On)
      Relay off;
  }
  else
  {
    if(Relay is Off)
      Relay on;
  }
  counter++; //increment by 1
}

//this method is more flexible than using a fixed number (30 minutes) because different heater controllers respond differently