A scientific article from the US National Institutes of Health titled The pathophysiological basis and consequences of fever gives a good review. From the abstract:
Where heat generation exceeds heat loss and the core temperature rises above that set by the hypothalamus, a combination of cellular, local, organ-specific, and systemic effects occurs and puts the individual at risk of both short-term and long-term dysfunction which, if severe or sustained, may lead to death.
It goes on to describe damage caused by fever in three main categories: (a) cellular damage, (b) localized effects (vascular stasis, inflammation response, etc), and (c) systemic effects. These are summarized in the following graphic:
Cellular damage
While direct cell death occurs around 41 C, protein and DNA synthesis is disrupted at lower temperatures. This means cells replicate more slowly (or not at all). This makes sense: your body normally achieves a fever state for fighting off infections, so activating your immune system and slowing down the ability for cell growth is helpful. Chronic, long-term fever would mean more stress on organs (including organ failure), a slower repair rate for bruises and broken bones, et cetera. It would also mean, with some caveats, a lower risk of infection (because foreign invaders would not be able to replicate as easily. Furthermore, gut flora would also have difficulty replicating which means more stomach aches and problems with digestion.
Localized effects
A slower blood flow (vascular stasis), increased risk for cancer (extravasation means white blood cells "leak" through the capillaries - good for fighting infections - but also means that cancer cells "leak" into different parts of the body), and overall inflammation. Inflammation means joint pain, muscle fatigue, digestive issues, increased risk of cholesterol blockage and therefore heart attacks, and, of course, organ damage or failure.
Systemic Effects
Gastrointestinal bacterial translocation means bacteria in your gut ends up elsewhere. The biotics in your gut help you break down food (literally do part of the digestion for you). These same bacteria in other areas besides the gut suddenly become dangerous foreign invaders. As such this could lead to not only more stomach issues (fewer bacteria in the gut) but bacterial infections caused by those bacteria being elsewhere. Furthermore, "endotoxemia" means stuff that's produced by the bacteria in your gut getting into the bloodstream. So not only does the bacteria end up elsewhere, but the stuff the bacteria produces gets dumped into the bloodstream, which is not good.
All of these effects kick on pretty quick (they can be measured after 30 minutes of mild fever in animal studies), and are inconveniences in the short term (up to a few days), but chronic, long-term damage would likely result in serious organ failure and death. The article goes on to describe damage to neurons (cognitive dysfunction), issues with the cardiovascular system, serious liver damage, haemostatic system issues (how the blood coagulates in muscles and damaged skin), and so on.
In heatstroke (which is temperatures above your quoted range), a 28-day mortality rate was 58%, and a whopping 71% at 2 years. Furthermore, 33% (one in three) survivors of heatstroke have some moderate to sever functional damage, and 41% requiring institutional care after a year. Granted, this would be temperatures above your quoted range, but I would anticipate similar issues with lower fevers at longer times (such as 10/15 years).
Take into account the increased rate of water and caloric expenditure, and decreased ability to metabolize food, and your people would have to eat and drink a lot while dealing with fatigue, mental issues, organ failures, and cancer.
