Voltage Comparator Circuit Output 0V or 5V

Do you even need +15V to -15V output???

Power on the speaker is ~Vpeak^2/R, so for an 8 ohm coil this system will blast out 15^2/8 ~= 28 Watts, which is pretty loud. Also placing DC current through a speaker is bad for it.

If you wanna stick with this design: you're going to need a Comparator with Rail-Rail operation, and even then that only gets you to Vdd-0.3V and Vss+0.3V . Check to see if this suits your needs. Since you are also driving a speaker, use Ohm's law on the speaker impedance to figure out how much current you're gonna need. An 8 ohm speaker will need at least a 2 Amp power supply for both +15 V and -15V. Best bet is to drive the system with +-18V 3A Rails. Find a comparator that can handle +-15V outputs, and get an output buffer that can handle 2 Amps both ways.

The LM741 has mV of offset. If you want to get an accurate comparison you could use a precision op-amp as a comparator. For example, an ADA4051.

If you're going to build this, I would like to see the source impedance a bit lower, maybe use a 10 ohm 1% resistor rather than 165 ohms and make the resistor that is now 100K something odd in the tens of K-ohms. Generally thermocouple instruments assume a source impedance in the 100 ohm range, at most, and most have noticeable error at 100 ohms.

Note that you are not doing cold-junction compensation (or, more accurately, cold junction emulation), so you'll not be able to get a good simulation of a thermocouple-- you'll get one (approximately) degree of error for every degree your terminal strip temperature is different from reference temperature. The 8.3(16)mV voltage you're using assumes a 32°F temperature- I hope you're warmer than that. At a 70°F CJC temperature, 8.3mV would give you about 438°F equivalent.