I mostly do hot process. Sodium lactate, when added after the cook, helps greatly in making the soap more fluid, whereas salt does not help with that. SL is also supposed to help cp soap firm up a bit faster so that it can be removed from the mold and cut sooner, but that's not a problem with my hp soaps. When I work with a fat that I know tends to make a a softer bar, such as black bear tallow, I dissolve a little salt in the water before adding the lye. Not too much, though. About 1/2 tsp. ppo is enough to make the bars firm. The first time I made soap with only bear tallow, I used 1 TBSP ppo. The bars were too hard and crumbly.
If I were purchasing beef tallow, I'd refrigerate any unused amount after opening the jar. When I render the fat myself, I know there is no water left in it, so I pour it into canning jars and do a boiling water bath to seal the jars. Then I just store at room temperature, even after opening a jar. I cook with it, so jars get used up pretty fast.