The search for signs of life is a major objective in the exploration of Mars. Of particular interest are chemical biosignatures such as biomolecules. However, molecular biosignatures are susceptible to extreme environmental conditions such as heat, ionising radiation and strong oxidants. Therefore, a knowledge of the stability of possible biosignature molecules under present and past conditions on Mars is important, as well as the nature of possible alteration products. In the light of the long volcanically active history of Mars, we have studied the thermal behaviour of selected biological compounds, namely, haemin (an iron porphyrin closely related to the haem prosthetic group), cytochrome c (a small protein) and lecithin (a mixture of phospholipids). Samples were exposed to temperatures up to 900°C under an inert atmosphere of nitrogen, either in neat form or in mineral matrices. The matrix materials used were sodium chloride, gypsum (CaSO4 ⋅ 2H2O), Ca-montmorillonite (STx-1b), the Martian regolith simulant JSC Mars-1A and some mixtures thereof. Key results are: (1) The onset of significant decomposition for haemin, cytochrome c and lecithin occurs around 240°C. At slightly higher temperatures the disappearance of all characteristic infrared spectral bands indicates complete decomposition and loss of the primary biosignatures. (2) Haemin stoichiometrically releases CO2 and HCl during the initial thermal decomposition phase, at the end of which the iron porphyrin core is still intact. High-temperature products of haemin include graphite, α-iron and cementite (Fe3C). (3) Neat lecithin forms long-chain polyphosphates at 500°C, whereas lecithin‒NaCl mixtures form diphosphate (pyrophosphate). As these anions are absent and rare, respectively, in minerals, they may potentially serve as secondary biosignatures. (4) Heating a mixture of NaCl and JSC Mars-1A at 800°C in the presence of lecithin produces the aluminosilicate mineral sodalite (Na8[AlSiO4]6Cl2), which however appears to be of limited use as a secondary biosignature.