[SalesForce] WhatId Is Not Available For Sending Emails To UserIds

I am getting the error – WhatId Is Not Available For Sending Emails To UserIds while trying to send email to user from an Apex Trigger using SingleMailMessage.

The code is working absolutely fine with a predefined standard EMail Template but the only problem is – it is unable to produce values of Merge Fields from the Custom Object that I wanted to set as whatId.

Any idea how to get rid of this error? As an alternative I might need to set the htmlBody of the mail in code but I am not sure.in that case how I can use the background layout that (it has some custom pink color and images set with company logo in the mail background)I had set in my email template?

   List<Messaging.SingleEmailMessage> eMail = new List<Messaging.SingleEmailMessage>(); 
   for (Event__c ea : eaList)
   {                   
    Set<String> invitedBy= new Set<String>();
    List<String> sendTo = new List<String>();  
    Messaging.SingleEmailMessage singleMail = new Messaging.SingleEmailMessage();

    invitedBy.add(ea.CreatedBy.Email);       // to capture unique values
    sendTo.addAll(invitedBy);
    singleMail.setToAddresses(sendTo);

    singleMail.setReplyTo('xxxx@gmail.com');
    singleMail.setSenderDisplayName('xxxx');
    singleMail.setTargetObjectId(ea.CreatedById);

    //set template Id
    singleMail.setTemplateId(et.Id);
    singleMail.setSaveAsActivity(false);
    // singleMail.setWhatId(ea.Parent_event_c);  // gives error WhatId Is Not Available For Sending Emails To UserIds
    eMail.add(singleMail);
}
Messaging.sendEmail(eMail);

I tried to follow the link – whatId when using custom object
and changed the code…but here I ended up doing DML (inserting contact) within for loop..any idea how to avoid this ?

 List<Messaging.SingleEmailMessage> eMail = new List<Messaging.SingleEmailMessage>(); 
   for (Event__c ea : eaList)
   {                   
    Set<String> invitedBy= new Set<String>();
    List<String> sendTo = new List<String>();  
    Messaging.SingleEmailMessage singleMail = new Messaging.SingleEmailMessage();

 // insert the mail id as a contact as suggested in the link 
tc = new Contact(email = ea.CreatedBy.Email, firstName = ea.CreatedBy.Name ,lastName = ea.CreatedBy.Name);
    insert tc ;
    invitedBy.add(tc.Email);       // to capture unique values
    sendTo.addAll(invitedBy);
    singleMail.setToAddresses(sendTo);

    singleMail.setReplyTo('xxxx@gmail.com');
    singleMail.setSenderDisplayName('xxxx');
    singleMail.setTargetObjectId(ea.CreatedById);

    //set template Id
    singleMail.setTemplateId(et.Id);
    singleMail.setSaveAsActivity(false);
    // singleMail.setWhatId(ea.Parent_event_c);  // gives error WhatId Is Not Available For Sending Emails To UserIds
    eMail.add(singleMail);
}
Messaging.sendEmail(eMail);
//delete the contact once email sent
delete tc;