In Acts 10, where Luke records the story of Peter’s vision of the unclean animals descending in a great sheet from heaven, I always regarded the reference to Peter’s hunger as a superfluous detail.
 The next day, as they were on their journey and approaching the city, Peter went up on the housetop about the sixth hour to pray.  And he became hungry and wanted something to eat, but while they were preparing it, he fell into a trance  and saw the heavens opened and something like a great sheet descending, being let down by its four corners upon the earth.  In it were all kinds of animals and reptiles and birds of the air.  And there came a voice to him: “Rise, Peter; kill and eat.”  But Peter said, “By no means, Lord; for I have never eaten anything that is common or unclean.”  And the voice came to him again a second time, “What God has made clean, do not call common.”  This happened three times, and the thing was taken up at once to heaven. (Acts 10:9-16)
The vision of animals descending on a sheet has a particular purpose as the Lord’s provision for Peter’s hunger. Peter is hungry, and so God tells him to rise, kill, and eat.
There is, then, an interesting parallel between this story and the story where Satan tempts Jesus in Luke 4:
[4:1] And Jesus, full of the Holy Spirit, returned from the Jordan and was led by the Spirit in the wilderness  for forty days, being tempted by the devil. And he ate nothing during those days. And when they were ended, he was hungry.  The devil said to him, “If you are the Son of God, command this stone to become bread.”  And Jesus answered him, “It is written, ‘Man shall not live by bread alone.’” (Luke 4:1-4)
In Luke 4, Jesus is hungry and so Satan tempts him with illicit food. Jesus resists the temptation.
In Acts 10, Peter is hungry and so God offers him (previously) illicit food. Peter resists God’s gracious provision, and he may even be thinking of Jesus’ temptation in the wilderness as he does so.
There are two key differences, though. First, God never tempts us to sin. Period. When God asks us to do something, we can trust that what he asks is not sinful.
Second, in Luke 4, Satan was trying to divert Jesus from his mission to the cross. In Acts 10, however, God was doing the exact opposite–he was expanding the proclamation of Jesus’ mission to the cross to the Gentile world.