I knew it had to be something simple. I found this article on Stackoverflow. I used the last answer for my custom webpart with the unigrid. Now I'm alble to use some jQuery plugins to get the table formatted for responsive layout.
protected override void OnPreRender(EventArgs e)
if ((gridTrans.GridView.ShowHeader == true && gridTrans.RowsCount > 0) || (gridTrans.GridView.ShowHeaderWhenEmpty == true))
gridTrans.GridView.HeaderRow.TableSection = TableRowSection.TableHeader;