An Open-label, 8-week Safety, Efficacy, and Assessment of Cooling Methods for Administration of CNTX-4975-05 for Knee OA

Key Inclusion Criteria: * Male or female subjects between 40 and 95 years of age (inclusive) * Confirmation of osteoarthritis (OA) of the knee: radiography of both knees using standard standing films (scored by the investigator) or using the fixed flexion method, taken during the Screening Visit of CNTX-4975i-OA-301 or CNTX-4975i-OA-304. * Confirmation of OA of the index knee: American College of Rheumatology (ACR) diagnostic criteria * For subjects for monoarticular knee injection, the index knee must have moderate to severe pain at screening associated with OA, which must be stable for a minimum of 6 months prior to Screening, as assessed by the investigator. These subjects may have: 1. unilateral or bilateral OA, with the index knee having moderate to severe pain, and the contralateral knee having none to mild pain, OR 2. unilateral or bilateral OA, with the index knee having moderate to severe pain and the other knee having had a PJR or TJR within 5 years of the Screening Visit. The knee with the PJR/TJR is not to be injected with CNTX-4975-05. For subjects for bilateral knee injection, the index knee must have moderate to severe pain at screening associated with OA, and greater pain in the index knee than in the contralateral knee. Their pain must be stable for a minimum of 6 months prior to Screening, as assessed by the investigator. The index knee in these subjects is the one with the worst pain with walking. Where both knees have equal pain with walking, then the knee on the subject's dominant side will be designated the index knee. For qualifying knee pain with walking, subjects will use an NPRS (0-10; 0=no pain, 10=worst possible pain) to rate their knee pain with walking (both knees, except knees with PJR/TJR). The PJR/TJR pain should be rated using the NPRS scale, but will not be a qualifying pain score. * Body mass index ≤45 kg/m\^2. Key Exclusion Criteria: * Joint replacement surgery of the index knee at any time, or open surgery of the index knee in the past 24 months. Joint replacement of the contralateral knee is permitted for subjects who will not receive an injection in the contralateral (natural) knee. * Prior arthroscopic surgery of the index knee within 6 months of Screening. * Any painful conditions of the index knee due to joint disease other than OA. Radicular or referred pain involving the index knee or from joint disease other than OA involving the index knee, such as, but not restricted to chondromalacia patellae, inflammatory d…