thank you for the good explanation.

typedef enum {
    I2C_ERROR_OK=0,
    I2C_ERROR_DEV,
    I2C_ERROR_ACK,
    I2C_ERROR_TIMEOUT,
    I2C_ERROR_BUS,
    I2C_ERROR_BUSY,
    I2C_ERROR_MEMORY,
    I2C_ERROR_CONTINUE,
    I2C_ERROR_NO_BEGIN
} i2c_err_t;

• when Wire.endTransmission() mean Wire.endTransmission(true), so success return I2C_ERROR_OK
• Wire.endTransmission(false) success return I2C_ERROR_CONTINUE

Do you know why the second part in "MLX90640_I2CWrite" worked?

int MLX90640_I2CWrite(uint8_t _deviceAddress, unsigned int writeAddress, uint16_t data)
{
  Wire.beginTransmission((uint8_t)_deviceAddress);
  Wire.write(writeAddress >> 8); //MSB
  Wire.write(writeAddress & 0xFF); //LSB
  Wire.write(data >> 8); //MSB
  Wire.write(data & 0xFF); //LSB
  if (Wire.endTransmission() != 0)
  {
    //Sensor did not ACK
    Serial.println("Error: Sensor did not ack");
    return (-1);
  }

I changed "MLX90640_I2CRead" to:

int MLX90640_I2CRead(uint8_t _deviceAddress, unsigned int startAddress, unsigned int nWordsRead, uint16_t *data)
{
  //Caller passes number of 'unsigned ints to read', increase this to 'bytes to read'
  uint16_t bytesRemaining = nWordsRead * 2;
  //It doesn't look like sequential read works. Do we need to re-issue the address command each time?
  uint16_t dataSpot = 0; //Start at beginning of array
  //Setup a series of chunked I2C_BUFFER_LENGTH byte reads
  while (bytesRemaining > 0)
  {
    Wire.beginTransmission(_deviceAddress);
    Wire.write(startAddress >> 8); //MSB
    Wire.write(startAddress & 0xFF); //LSB
    if (Wire.endTransmission(false) != 7) //Do not release bus
    {
      Serial.println("No ack read");
      return (0); //Sensor did not ACK
    }
    uint16_t numberOfBytesToRead = bytesRemaining;
...

• Wire.endTransmission(false) run ok will return 7, not 0

• It is necessary to take new arduino library. @heybin: Thanks.
• Problem with "MLX90640_I2CRead". I changed this in the function:

   /*
    if (Wire.endTransmission(false) != 0) //Do not release bus
    {
      Serial.println("No ack read");
      return (0); //Sensor did not ACK
    }*/
    Wire.endTransmission(false);

Now it worked for me.