It's an "Access to modified closure" problem. Look into that for more details. There's a lot of examples of what it is.
Simple fix is to store your n variable in a temp variable everywhere you use it in your delegate.
foreach (int n in arrMessageid)
{
int tempN = n;
Thread thrdSendEmail = new Thread(() =>
{
try
{
amazonMessageID = SendSimpleEmail_Part2(messageAmazonRequestBatch.ElementAt(tempN ).req);
messageAmazonRequestBatch.ElementAt(tempN ).msg.AmazonMessageID = amazonMessageID;
logManager_MessageLogwithAmazonmsgID.LogMessage(",\t" + tempN , true);
//logManager_MessageLogwithAmazonmsgID.LogMessage(",\t" + tempN + ",\t" + messageAmazonRequestBatch.ElementAt(tempN ).msg.QueueMessageId + ",\t" + amazonMessageID, true);
}
catch (Exception ex) { logManager_RunSummary.LogMessage(ex.Message, true); }
});
thrdSendEmail.Name = n.ToString();
lstThread.Add(thrdSendEmail);
thrdSendEmail.Start();
//logManager_MessageLogwithAmazonmsgID.LogMessage(",\t" + n, true);
}