I received my refund, via direct deposit, for the correct amount. I have now received a check from the US Treasury. No letter enclosed. Why did I get this check?

That is weird.   It probably isn’t interest is it?  Does it say anything near the bottom of the check like INT?   You should get a separate letter explaining it.   Or call the IRS.   Is it a big amount?  Did you miss entering an estimated payment or something?   

The letter of explanation comes days or weeks after the check.

That's how IRS operates.

@stangwizdak