Far be it from me to question the opinions of learned scholars on the matter of Alexander's death, but please allow me to quote from one of the very few sources we have available from antiquity, the excellent "Anabasis of Alexander" from Arrian, who had access to many primary source materials:
"Not many days later Alexander offered the gods the customary sacrifices for good fortune ... and then began feasting with his friends and drinking far into the night. ... He drank and made merry with Medius, and then, after rising and bathing, went to sleep; he afterwards dined with Medius, and again drank until late in the night, and then breaking off from the carouse bathed, and after bathing ate a little and slept just where he was, as he was already in a fever." --Anabasis, VII 24.4 - 25.1

This is the fever that would, a few days later, kill him. Arrian claims to draw this account from a royal "journal" that was made by Alexander's courtiers, but this is probably spurious. Nevertheless, this account (which is strikingly similar to one given by Plutarch and seemingly based on some testimony of Medius and the Companion Nearchus) is probably the best evidence we have for Alexander's mode of death. Certainly, the fever may have been caused by something other than the near-continuous cycle of drinking and bathing, but Arrian considers these activities causal.