ESP8266 can't detect DS18B20 Temperature Sensor

Since you don't a DMM, let's use use the ESP8266 to measure the voltage on the DS18b20 output.
Temporarily connect the DS18b20 output (your yellow wire) to A0 and run this code. The ADC value should be close to 1023.


const int analogInPin = A0;  // ESP8266 Analog Pin ADC0 = A0

int ADCValue = 0;

void setup() {

  Serial.begin(115200);
}

void loop() {
  // read the analog in value
  ADCValue = analogRead(analogInPin);

  // print the readings in the Serial Monitor
  Serial.print("ADC = ");
  Serial.println(ADCValue);

  delay(1000);
}