Ytdyklly

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?

The claim is false, as evidenced by Prospective Evaluation of the Risk of Serious Bacterial Infection in Children Who Present to the Emergency Department With Hyperpyrexia (Temperature of 106°F or Higher) Pediatrics, July 2006; 118(1): 34–40.

Data were collected prospectively on all children <18 years of age presenting to a pediatric emergency department during a 2-year period with rectal temperatures of ≥106°F

...

Of 130 828 visits, 103 children had hyperpyrexia (1 per 1270 patient visits). Of the 103 subjects, 20 had serious bacterial infection, and 22 had laboratory-proven viral illness (including 1 subject with bacterial/viral coinfection)

...

Common causes of hyperpyrexia in children include bacterial infections, viral infections...

...

One subject, a 4-year-old boy with muscular dystrophy, presented with both neuroleptic malignant syndrome and apparent septic shock. His temperature reached 108.9°F, and he expired during subsequent hospitalization despite aggressive management. A tracheal aspirate collected in the ED grew Pseudomonas. Because the same organism was recovered from autopsy blood cultures, the Pseudomonas was regarded as the cause of sepsis.

...

no child arrived in the ED with hyperpyrexia secondary to heat-related illness