I apologize, I may have misunderstood your meaning of heat stability in the context of preservatives.  Sodium benzoate can be decarboxylated in the presense of a base and heat, yielding the dangerous chemical benzene, so regarless of effectiveness, sodium benzoate is only used in foods that are not basic pH (i.e. used only in foods that are acidic).  

However, acidic enviroments are not always safe either.  In combination with ascorbic acid (vitamin C, E300), sodium benzoate (and its replacement potassium benzoate) may form benzene. In 2006, the Food and Drug Administration tested 100 beverages available in the United States that contained both ascorbic acid and benzoate. Four had benzene levels that were above the 5 ppb Maximum Contaminant Level set by the Environmental Protection Agency for drinking water. Most of the beverages that tested above the limit have been reformulated and subsequently tested below the safety limit. Heat, light and shelf life can increase the rate at which benzene is formed. Hot peppers naturally contain vitamin C ("nearly as much as in one orange") so the observation about beverages also applies to pepper sauces containing sodium benzoate. 

Sodium benzoate may react with other additives in food, as well.  Research published, including in 2007 for the UK's Food Standards Agency (FSA) suggests that certain artificial colors, when paired with sodium benzoate, may be linked to hyperactive behavior and other ADHD symptoms. The results were inconsistent regarding sodium benzoate, so the FSA recommended further study. The Food Standards Agency concluded that the observed increases in hyperactive behavior, if real, were more likely to be linked to the artificial colors than to sodium benzoate. The report's author, Jim Stevenson from Southampton University, said: "The results suggest that consumption of certain mixtures of artificial food colours and sodium benzoate preservative are associated with increases in hyperactive behaviour in children. . . . Many other influences are at work but this at least is one a child can avoid."

Benzene is classified as a carcinogen, which increases the risk of cancer and other illnesses, and is also a notorious cause of bone marrow failure. Substantial quantities of epidemiologic, clinical, and laboratory data link benzene to aplastic anemia, acute leukemia, bone marrow abnormalities and cardiovascular disease. The specific hematologic malignancies that benzene is associated with include: acute myeloid leukemia (AML), aplastic anemia, myelodysplastic syndrome (MDS), acute lymphoblastic leukemia (ALL), and chronic myeloid leukemia (CML).

The American Petroleum Institute (API) stated as early as 1948 that "it is generally considered that the only absolutely safe concentration for benzene is zero". There is no safe exposure level; even tiny amounts can cause harm. The US Department of Health and Human Services (DHHS) classifies benzene as a human carcinogen. Long-term exposure to excessive levels of benzene in the air causes leukemia, a potentially fatal cancer of the blood-forming organs. In particular, acute myeloid leukemia or acute nonlymphocytic leukemia (AML & ANLL) is caused by benzene. IARC rated benzene as "known to be carcinogenic to humans" (Group 1).

As benzene is ubiquitous in gasoline and hydrocarbon fuels that are in use everywhere, human exposure to benzene is a global health problem. Benzene targets the liver, kidney, lung, heart and brain and can cause DNA strand breaks and chromosomal damage. Benzene causes cancer in animals including humans. Benzene has been shown to cause cancer in both sexes of multiple species of laboratory animals exposed via various routes.

Potassium sorbate, may be a safer option, as it does not degrade into benzene.  However, the upper pH limit for its effectiveness is 6.5, due to decreasing effectiveness against molds at higher pH.

As a food additive, potassium sorbate is used as a preservative in concentrations of 0.025–0.100%, which in a 100 g serving yields an intake of 25–100 mg. In the United States, no more than 0.1% is allowed in fruit butters, jellies, preserves, and related products. Up to 0.4% has been studied in low-salt, naturally-fermented pickles, and when combined with calcium chloride, 0.2% made "good quality pickles." Potassium sorbate has about 74% of sorbic acid's anti-microbial activity. When calculated as sorbic acid, 0.3% is allowed in "cold pack cheese food."

The maximum acceptable daily intake for human consumption is 25 mg/kg, or 1750 mg daily for an average adult (70 kg). Under some conditions, particularly at high concentrations or when combined with nitrites, potassium sorbate has shown genotoxic activity in vitro.
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