removing delay() in DallasTemperature.cpp

My project require the use of a Dallas temperature sensor and the my program already execute other functions that can not be delayed at all. The Dallas need a 1 second delay everytime a request is made. How DallasTemperature.cpp program can be modified to not use delay() but millis() instead ?

http://milesburton.com/downloads/Arduino/DallasTemperature/DallasTemperature.rar

// Send command
void DallasTemperature::beginCommunication(void)
{
  pDataWire->reset();
  pDataWire->select(arSlaveAddr);
  pDataWire->write(STARTCONVO,1);         // start conversion, with parasite power on at the end
  delay(1000);
}

You could save the current millis() value and add 1000 (although 750 will be fine) to it after the StartConversion has been commanded. Afterwards, the Arduino can continue doing what it needs to do, periodically checking the value of millis() to see if the delay has expired, and read the temperature then. The temperature value will be retained by the 18x20 until the Arduino has a chance to read it.