In the studio we often use strobes or continues lighting (depending on your preference)
Most continuous lighting is daylight balanced just like strobes (well approximately). However the modeling lights of your strobes are not. They are in most cases very warm because they are in fact tungsten.
This could go you the impression you can’t mix those two. Well you can of course mix strobes (that fire) with continuous. But why not combine the modeling lights with continuous lighting and create some cool effects.
I love for example to use our ledgo or lumecubes on the face of the model and use the modeling lights to light the whole scene. Now combine this with even warmer light like in this shot and you have a “mess” of color temperatures but when you mix them together with some thought you get some really cool effects.