I think you're getting the wrong idea here.

Diogenes Laertius 6.2.22 talks about Diogenes' habit of going about his daily business outdoors. He says that Diogenes' letters--because Diogenes Laertius claims Diogenes wrote some 21 works, including 7 tragedies, though two of his sources he says insist that Diogenes wrote nothing at all and one claims that the tragedies are really terrible and were actually by his friend--explain that Diogenes had told someone to go buy him a house. When the dude took too long Diogenes found a pithos, basically a really big amphora, near the Metroon in Athens to sleep in. Diogenes Laertius mentions the pithos again later on, at 6.2.43, where the Athenians grew to be so fond of Diogenes that they bought him another pithos with public money when a boy broke his.

It's not even certain, though, where Diogenes lived in his pithos. Diogenes Laertius places him in Athens, and though he mentions him also living later at the Craneum in Corinth he doesn't say anything about how he lived, and seems to suggest that he would just kind of lie out in the open wrapped in his cloak. But Lucian at Hist. Conscr., 3 says that when Philip was marching on Corinth and everybody was running around arming themselves and preparing for war Diogenes, who was then living there, started rolling his pithos up and down the Craneum, ostensibly because he didn't want to look like an idler while everybody else was so busy.