Why don't allergies cause fever?
The short answer seems to be that fevers help combat microbes (a term I take herein to include viruses for brevity), which aren't a part of the threat addressed in an allergic reaction. While there's not a full consensus on which benefits, if any, a fever brings to the response to microbes, both humans and other warm-blooded vertebrates fare better with infections when a fever is present.

Fevers appear to mobilise leukocytes and enhance their phagocytosis while suppressing endotoxin effects (see Craven, R and Hirnle, C. (2006). Fundamentals of nursing: Human health and function. Fourth edition. p. 1044) and proliferate T cells (see Lewis, SM, Heitkemper, MM, and Dirksen, SR. (2007). Medical-surgical nursing: Assessment and management of clinical problems. sixth edition. p. 212), rather than mobilising basophils.

Higher temperatures are also more damaging to at least some pathogenic cells than the body's own, as they are typically smaller with higher relative surface area. Note this also explains why fevers wouldn't be as natural a response to such large parasites as helminths. (Even their cells, being eukaryotic, are comparable to human cells.) It is unsurprising that IgE would be a more specialised response, found only in mammals.

On the subject of malarial fever, for which the pathogen is relatively large because it is eukaryotic, there is ongoing research into both the mechanism and function of this fever. It seems to be Plasmodium itself that creates and presumably benefits from the fever, not the host. I'll discuss the evidence in a moment, but note this means the "endogenous fevers follow suspected small pathogens" hypothesis is unthreatened.

According to this 2013 paper, the timing of such ruptures may (I stress may; the paper discusses the uncertainty around a number of ideas about this) serve the function of controlling the time at which the immune response is most active, so the reproductive cycle is unaffected. According to this 2007 paper, the malarial parasite's hemozoin causes the disease's characteristic fever following erythrocyte rupture. The same paper mentions that the timing of the fever has been used as a diagnostic criterion for malaria, and the 1927 Nobel Prize for Medicine was awarded for the now discontinued treatment of syphilis with a malaria-induced fever.