This question is prompted by but distinct from Is fever (temperature) below 106° F harmful? That question asks about whether fevers below that temperature can cause harm. This question is asking whether there is any appreciable risk of fevers below that temperature progressing to higher temperatures when the underlying cause of fever is a bacterial or viral infection.
That question quotes a source that says in a very definitive tone that fevers caused by viral or bacterial infections do not go above 105 °F:
The common cold and influenza are the most common sources of elevated temperatures.. they can generate fevers that range all the way up to 105 degrees, but [...] Untreated fevers caused by viral and bacterial infections do not rise inexorably and will not exceed 105 degrees [...]
Only in the case of heatstroke, poisoning, or other externally caused fevers is this bodily mechanism over-whelmed and inoperative. It is in those cases that temperatures reach and exceed 106 degrees
(How to Raise a Healthy Child in Spite of Your Doctor, Robert S. Mendelsohn, as quoted in alpha1's question)
Is it true that infections are a negligible cause of elevated body temperature above 105 °F?