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Временный в данном контексте мне не встречался. Обычно либо chronic periodontitis, либо без chronic. Есть local/localized periodontitis - Ectopic gingival sebaceous glands presenting as localized ...1990 Jan;61(1):58-60. Ectopic gingival sebaceous glands presenting as localized periodontitis. Cohen RE, Aguirre A, Drinnan AJ, Neiders ME, Mastroianni AJ. ...
www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve& db=PubMed&list_uids=2313524&dopt=Abstract

Есть periapical periodontitis -
Periapical periodontitis is an infection that can affect the tooth and its surrounding tissues and can cause tooth ache
http://www.users.dircon.co.uk/~toothyp/pages/endodontist1.ht...

Еще есть разделение на adult and juvenile periodontitis, а также выделяют acute periodontitis: Official Patient's Sourcebook on PERIODONTITIS (acute periodontitis; chronic
periodontitis; pyorrhea gum disease; severe gum disease; severe gum inflammation). ...
www.icongrouponline.com/health/Periodontitis.html

Параллельно существуют степени - mild, moderate, and severe:

Untreated gingivitis leads to mild periodontitis. This stage
of gum disease shows evidence of the bone around the tooth starting to erode. ...
web1.tch.harvard.edu/cfapps/A2ZtopicDisplay. cfm?Topic=Periodontal%20Disease