No, increasing the temperature on your AC will not make it colder. In fact, it will do the opposite. The temperature setting on your air conditioner controls the target temperature at which the AC will maintain the indoor environment. When you set the temperature higher, it means you're telling the AC to cool the room to a higher temperature, making it warmer.
To make the room colder, you should set the temperature lower, so the AC will work to cool the air to a lower temperature. For example, if you want the room to be cooler, you should lower the temperature setting on the AC, like setting it to 72°F (22°C) instead of 78°F (26°C). This will prompt the AC to work harder to achieve the lower temperature you desire.