Five varieties of vegetable oil underwent oleogelation with two types of wax as follows: beeswax (BW) and rice bran wax (RW). The oleogels were analyzed for their physicochemical, thermal, and textural characteristics. The oleogels were used in the bun dough recipe at a percentage level of 5%, and the textural and rheological properties of the oleogel doughs were analyzed using dynamic and empirical rheology devices such as the Haake rheometer, the Rheofermentometer, and Mixolab. The thermal properties of beeswax oleogels showed a melting peak at a lower temperature for all the oils used compared with that of the oleogels containing rice bran wax. Texturally, for both waxes, as the percentage of wax increased, the firmness of the oleogels increased proportionally, which indicates better technological characteristics for the food industry. The effect of the addition of oleogels on the viscoelastic properties of the dough was measured as a function of temperature. All dough samples showed higher values for G′ (storage modulus) than those of G″ (loss modulus) in the temperature range of 20–90 °C, suggesting a solid, elastic-like behavior of all dough samples with the addition of oleogels. The influence of the beeswax and rice bran oleogels based on different types of vegetable oils on the thermo-mechanical properties of wheat flour dough indicated that the addition of oleogels in dough recipes generally led to higher dough stability and lower values for the dough development time and those related to the dough’s starch characteristics. Therefore, the addition of oleogels in dough recipes inhibits the starch gelatinization process and increases the shelf life of bakery products.