Cognitive radio networks (CRNs) are composed of unprivileged users as called secondary users (SUs) that utilize the spectrum opportunities produced by the absence of co-located privileged primary users (PUs). Providing a certain level of quality of service (QoS) to these SUs is a very challenging problem as these users are constrained strictly by PU arrivals. Many existing works tackled this problem by centralized and complex optimization techniques and complex mac layer protocols. As opposed to the existing QoS management schemes, in this paper, we propose a fast, distributed, PU temporal activity estimation aided spectrum assignment scheme for the SUs with traffic demands at different QoS levels. We designed our heuristic method by leveraging low prioritized (LP) packets over high prioritized (HP) packets on channels in heavy use in terms of temporal PU activity and used the opposite manner for the channels being in sparse use. We modeled our proposed scheme along with the network model we employed in MATLAB (R) and evaluated its performance with respect to a native scheme that utilities every spectrum opportunity for the HP traffic. Our simulations validated the effectiveness of the proposed channel assignment scheme in terms of Figure of Merit metric we defined reflecting the weighted sum of the throughput ratio values for packets of different QoS levels that successfully reached at the destination SU.