Among common causes of rhinitis are
One way to disentangle between infection and allergy in presence of rhinitis is by the presence/absence of fever. Indeed, allergies never triggers fever (see Why don't allergies cause fever?), while infections often do.
Can non-allergic, non-pathogenic rhinitis (e.g. irritant and weather change) also be associated with fever?
Common cold, which is an acute viral infection of the nose, is rarely associated with fever in adults (Canadian Medical Association Journal ; DPHHS Montana).
Allergic rhinitis does not usually cause fever; it's not mentioned as a symptoms on major clinical websites (Emedicine ; Mayo Clinic ; MedlinePlus). News In Health says allergic rhinitis "never" causes fever, while The Journal Of Allergy and Clinical Immunology says that fever "is rarely found in patients with allergic rhinitis."
Non-allergic rhinitis (irritant, vasomotor, hormonal, medicamentous, gustatory, senile, etc.) is also not associated with fever according to various sources (Emedicine ; Mayo Clinic ; World Allergy Organization ; Allergy). After some further research, there seems to be no evidence that non-allergic, non-infectious rhinitis would be associated with fever, but I can't exclude the possibility that sometimes could be.
In conclusion, the absence of fever does not help (much) in determining the type of rhinitis.
