We reanalyze the conditions under which we have a primordial thermal population of axions .
We extend a previous study and take into account processes involving gluons and quarks .
We conclude that if the Peccei-Quinn scale fulfills F _ { a } < 1.2 \times 10 ^ { 12 } GeV there is thermal axion production .
In this case , a period in the early universe exists where axions would interact with the QCD plasma and we point out that non-thermal axions produced before the end of this period would thermalize .