The Mars Atmosphere and Volatile EvolutionN (MAVEN) spacecraft can act as an intermittent upstream solar wind monitor at ~ 1.5 AU. To inspect the evolution of solar wind turbulence in the Martian exosphere, we have gathered proton (i.e., ionized hydrogen) temperature measurements taken by the Solar Wind Ion Analyzer (SWIA) onboard the MAVEN spacecraft. Here we investigate instabilities driven by the proton temperature anisotropy at Mars. We look at the temperature anisotropy T_⊥p/T_||p (i.e., the ratio of the perpendicular proton temperature component to the parallel proton temperature component) and the parallel plasma beta, β_||p, to determine the active plasma instability mode. Furthermore, we report on the properties of turbulence near Mars’ orbital location during upstream solar wind intervals from January 2015 to December 2016 (~ 1 Martian year). We find that the probability distributions of (β_||p, R_p)-values are limited at R_p >1 and R_p <1. We also find evidence of intermittency implying nonlinear, non-homogeneous energy transfer. Additionally, spectral index values near the Kolmogorov scaling value are observed for the inertial range (10^-4 Hz to 0.1 Hz).