This has also been my experience. I often take naps around the same time and find that the nap calms me naturally and sort of distances me from any anxieties surrounding a problem I'm trying to tackle. This makes it much easier to work at it some more.
Separately I noticed that if I have any symptoms of depression (usually thoughts of despair), a nap like that can by itself often completely reverse the situation. Surprised, I did some research and was interested to find how much a lack of proper rest is associated with depression. So now the first item on my "feeling depressed" checklist is "try to take a nap".