In the definition of the temperature load have you selected just faces of the model or the entire model body? I ask because if you only have faces selected then the interior volume will have its temperature set to 0 Kelvin because the interior nodes can't have a null value. This could wreak havoc with your results and possibly cause convergence warnings like you appear to have.
Thank you for the feedback. I did as you suggested and the analysis finished. The results weren't all that great, but that's more of a setup problem. Thanks again.