In this paper, changes in the textural properties of butternut squash caused by thermal treatment in a convection steam oven with different levels of temperature, steam, and different process durations were considered. Textural properties of pumpkin pulp were measured in terms of five features (characteristics): hardness, chewiness, gumminess, springiness, and cohesiveness. Pearson’s correlation coefficients for measurements of the characteristics indicated significant linear relationships at a significance level of 0.05. This fact justified the use of multivariate statistical methods to explore the simultaneous impact of temperature, steam, and time on textural attributes of butternut squash. Shapiro–Wilk tests did not disprove the normality of four textural characteristics; namely, hardness, springiness, gumminess and chewiness. Based on the measurements of the four above normally distributed features, three-way multivariate analysis of variance with all double interactions between the factors proved their significant impact on textural properties of butternut squash pulp at a significance level of 0.05. Additionally, applied multivariate techniques such as canonical correlation analysis, principal component analysis, factor analysis, clustering analysis, and discriminant analysis explained relationships between the factors and characteristics under consideration.