Growers in the cultivated areas where the climate change threatens the agricultural productivity and livelihoods are aware that the current constraints for good quality water are being worsened by heatwaves. We studied the combination of salinity (60 mM NaCl) and heat shock stress (43 °C) in pepper plants (Capsicum annuum L. var. Tamarin) since this can affect physiological and biochemical processes distinctly when compared to separate effects. Moreover, the exogenous application of 0.5 mM salicylic acid (SA) was studied to determine its impacts and the SA-mediated processes that confer tolerance of the combined or stand-alone stresses. Plant growth, leaf Cl− and NO3− concentrations, carbohydrates, and polyamines were analyzed. Our results show that both salinity stress (SS) and heat stress (HS) reduced plant fresh weight, and SA only increased it for HS, with no effect for the combined stress (CS). While SA increased the concentration of Cl− for SS or CS, it had no effect on NO3−. The carbohydrates concentrations were, in general, increased by HS, and were decreased by CS, and for glucose and fructose, by SA. Additionally, when CS was imposed, SA significantly increased the spermine and spermidine concentrations. Thus, SA did not always alleviate the CS and the plant response to CS cannot be directly attributed to the full or partial sum of the individual responses to each stress.