In new slim torque converters, lock-up clutches are used to provide high fuel efficiency at low speed. However, the slimness of the converters causes difficulty in heat dissipation, which may damage the friction material and shorten its life span. A cooling hole in the lock-up piston reduces the heat but also reduces the torque because oil flows through the hole due to the pressure difference between the two faces of the piston. In the early stages of the development of this type of torque converter, designers must consider the minimum flow rate required to cool the friction material and the minimum torque capacity required to transmit the engine torque. This research explored two methods of estimating these parameters. In the first method, an estimation equation was derived by combining the response surface method with physical properties such as the centrifugal force, a sudden expansion, a sudden contraction, and the steady flow energy equation. The second method involved the use of an artificial neural network. The feasibility of the estimates based on statistics and on the artificial neural network were confirmed in the design stage by comparing experimental and estimated data. An estimation program was created using the C#.Net language and has been used for actual torque converter designs by the Korea Powertrain Company.