Long story short, both dōmo arigatō and doumo arigatou are acceptable.
Let's take a look of how this phrase is spelled out in Japanese:
どうもありがとう, where each character is read as do-u-mo-a-ri-ga-to-u.
When put together, it becomes doumo arigatou.
However, /ou/ sequences in Japanese are usually pronounced as a long o, which is written as ō. This means that dōmo arigatō is also correct.
The convention to write /ou/ as ō (o with a macron) is based on Hepburn romanization, the most-widely used Japanese romanization published by James Curtis Hepburn in 1867.
On the other hand, domo arigato, without the use of ō is... not quite right, because it does not capture the essence of /ou/ that is present in the Japanese script. If transliterated back into Japanese, domo arigato would surface as どもありがと (incorrect) instead of どうもありがとう (correct).
So, stick to either doumo arigatou, dōmo arigatō, or どうもありがとう.
