It's not actually a schematic, but it does indicate how you have wired things up, so thanks for that.
Try this change:
int thermoDO = D7;
int thermoCS = D6;
int thermoCLK = D5;
...
const int IN1_PIN = D3; // the Arduino pin connected to the IN1 pin L298N
const int IN2_PIN = D4; // the Arduino pin connected to the IN2 pin L298N
On ESP based Arduino, "D5" is not the same as "5". There are two different pin numbering schemes in play!
Hopefully the above will allow the esp to communicate with the max6675 and prevent the watchdog errors.
It is believed that the L298 module purchased may have a built-in 5V regulator. @emonter will confirm that when their new DMM arrives.
I recommended that the max6675 be powered with 3.3V. What's your opinion?