The objective of this study was to assess the effect of storage temperature on the fresh sperm quality of Steindachneridion parahybae over 112 h of storage. Semen collected from five males was tested in a 12 × 4 factorial experimental design using the sperm storage times of: 0 (control), 1, 2, 4, 8, 16, 24, 36, 48, 64, 88, and 112 h after collection. Temperatures tested were (mean ± SD): 5.2 ± 3.4, 12.9 ± 1.6, 24.4 ± 1.7 and 34.9 ± 1.1°C. Sperm parameters were motility rate (MOT), curvilinear velocity (VCL), average path velocity (VAP), straight line velocity (VSL), straightness (STR), sperm normality (NOR) and survival rate (SUR). The parameters VCL, VAP and VSL were grouped by principal component analysis to create the sperm velocity (VS). The parameters assessed exhibited effects (P < 0.05) of the exposure time and temperature. Interactive effects between temperature and time (P < 0.05) were observed for STR, NOR and SUR, and quadratic effects for factors MOT and VS (P < 0.05). Pearson's linear correlation was verified between the parameters studied (P < 0.05), indicating MOT, VCL and STR as good indicators of sperm quality. Chilling at temperatures around 5°C and heating at around 35°C were harmful to S. parahybae spermatozoa. It is suggested that short‐term (up to 8 h) semen storage – if necessary – should be within a range of 15–25°C.