How can I control TRIAC firing angle automatically with a DC voltage?
Your best solution may be to use an opto-isolated Triac driver to drive the power Triac and achieve ON off control with galvanic isolation and low EMI from the built in zero-crossing switch (ZCS).  

Since the slew rate of temperature is slow, no DC controlled pulse is required. It will cycle on and off and regulate to whatever set point you choose with an LDO derived Vref with a comparator  and filter cap.  The opto-triac is just needs 5 to 10mA active low from the comparator with a current limiting R for the ~ 2.1V IR diode with Anode to LDO. You can use 3.3 to 5V for the LDO.

Hysteresis or temperature error depends on the stability of Vref and external AC noise level of temp sensor voltage to ADC as excessive noise may cause  it to cycle on and off quickly from a sensitivity of  10mV/degC. Noise reduction methods include, RC filter  from twisted pair or coax as shown in data sheet. Series R and 50pF max or larger R and bigger C. 

Temp errors will only occur if the noise is pulse like and not symmetrical.  If symmetrical AC hum exists on the temp signal, the Triacs will just  cycle on and off at equilibrium like a cycle  based PWM. 

Other small sources of error may  be from lack of thermal insulation outside sensor and poor conductance to the medium from the outside wall and/or the thermal insulation of the container with minimum thermal difference from heater end  to opposite end.

Summary

You  may  choose Opto-triac, Triac with thermal resistance and temp rise  at  rated current, LDO, pot, comparator, RC filters, cables, connectors, and have an indicator which could be a 2V Red LED in series with IR LED which affects series R (voltage drop I=V/R) to get the  same 10mA max current.  Have fun.