Remus Lupin used the same trunk as a Professor that he used in his Hogwarts' days as a student. The trunk was very old, it had peeling letters forming the name tag Prof. Remus J. Lupin and those letters were pasted there by his friends in their fifth year when Rem had first told them that he would love to come back to school as a teacher some day.

That was probably the reason he took the train to school instead of flooing in like the other teachers. He just had so many memories that he would be reliving and didn't want to miss out on any of them even though it was painful considering that none of his friends were with him at that time.