A Dream Deferred by Langston Hughes

How is the Hugh's poem "A Dream Deferred " reflected in Martin Luther King's "I have a dream"speech?

Are they talking about the same dream?

"So even though we face the difficulties of today and tomorrow, I still have a dream. It is a dream deeply rooted in the American dream. I have a dream that one day this nation will rise up and live out the true meaning of its creed: We hold these truths to be self-evident, that all men are created equal."

"I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression will be transformed into an oasis of freedom and justice."
How do both King and Hughes use the idea of heat in their writing?

"This sweltering summer of the Negro's legitimate discontent will not pass until there is an invigorating autumn of freedom and equality. 1963 is not an end, but a beginning. Those who hope that the Negro needed to blow off steam and will now be content will have a rude awakening if the nation returns to business as usual."

What does this text from King's speech have in common with the last line of "A Dream Deferred"? Are these warnings from both King and Hughes? Did both these men feel this unrest in their communities?