I believe you are going wrong by not subtracting the zero degree C. offset before you calculated the final value of quanta. Here is what I calculate:

0 degrees C. = 273.15 degrees K.
273.15 degrees K. x .01 volts = 2.7316 volts @ 0 degrees C.
5 volts / 1023 counts = .004887586 volts per count
2.7315 volts / .004887586 volts per count = 588.86484 counts
588.86484 raw counts = 0 degrees C. = 273.15 degrees K.

After subtracting the 588.86 counts from the raw reading, you end up with:
.01 volts per degree C. / .004887586 volts per count which equals 1 degree C.