How to change height of grouped UITableView header?

Return CGFLOAT_MIN instead of 0 for your desired section height.

Returning 0 causes UITableView to use a default value. This is
undocumented behavior. If you return a very small number, you
effectively get a zero-height header.

Swift 3:

 func tableView(_ tableView: UITableView, heightForHeaderInSection section: Int) -> CGFloat {
        if section == 0 {
            return CGFloat.leastNormalMagnitude
        }
        return tableView.sectionHeaderHeight
    }

Swift:

func tableView(tableView: UITableView, heightForHeaderInSection section: Int) -> CGFloat {
    if section == 0 {
        return CGFloat.min
    }
    return tableView.sectionHeaderHeight
}

Obj-C:

    - (CGFloat) tableView:(UITableView *)tableView heightForHeaderInSection:(NSInteger)section
{
    if (section == 0)
        return CGFLOAT_MIN;
    return tableView.sectionHeaderHeight;
}