Assuming dark matter wasn't created cold enough to cluster on those scales, then yeah, that's a fair interpretation. However it should be noted that on galactic scales, the temperature of the dark matter was not the limiting influence on when structures began to form. That was set by the initial amplitude of variations in the density of the universe and the details of how they grew over time (which are determined by certain aspects of the history of the universe).

Since the dark matter temperature was not the limiting influence, we actually have no clear evidence what its temperature initially was. However, by probing dark matter halos at smaller and smaller scales, we might be able to determine it. The impact of temperature becomes more important at smaller scales.