You don't need PWM or an H-bridge if you're aiming for a 10 degree C range of temperature. Heat doesn't move quickly enough to warrant that level of control; you could be switching this off/on once a second and still be way ahead of the accuracy of your temperature sensor. An H-bridge also suggests you'll be reversing the current to the peltier and I don't think you'll be doing that. Finally, peltiers do lose a little
efficiency if you PWM them so it's not really an ideal way to go.
Do you know how many watts of heat your camera sensor generates (which would be closely related to how much it takes to power it)? Your peltier will need about 10 times that much power to cool that heat. While the peltier might accept a hundred watts of power it's doubtful you'll need to power it to that extent if you're just negating the heat from a few LEDs and the ambient temperature.
Instead of a thermistor look into using a LM335
). These are both very popular temperature sensors and won't require the calibration that a thermistor would -- and they're cheap.