[cflsystems]

The info is available there

/skin/common_files/customer/main/order_message.tpl

You have to do something like

{foreach from=$orders item=order}
{if $order.paymentid eq "xxx"}
show message1
{elseif $order.paymentid eq "yyy"}
show message2
{else}
show message3
{/if}
{/foreach}