With current version of Angular Material (6.4.7) you can use a custom class:
let dialogRef = dialog.open(UserProfileComponent, {
panelClass: 'my-class'
});
Now put your class somewhere global (haven't been able to make this work elsewhere), e.g. in styles.css
:
.my-class .mat-dialog-container{
height: 400px;
width: 600px;
border-radius: 10px;
background: lightcyan;
color: #039be5;
}
Done!