Is there an ideal air temperature for best performance in a light aircraft? I know cold air is better for engine performance in general, colder air is also denser making lift components stronger(from what I understand). 

I was just wondering if there is a temperature or a range of temperatures that offer the best performance overall?

Is there a temp that covers all areas such as takeoff/climb performance, cruise etc. or is it something where each performance area has its own "sweet" spot? 

Let's use common flight trainers like the C172 as the example.
Good Evening Alex,
just for the record I'm a Private Pilot with about 150 hours of flight time, I would recommend speaking to a Flight instructor if you have any more questions about Aircraft POF. (principles of flight and performance) 

Best Performance can be narrow down to a simple formula  
Best Performance = High Pressure + Low Temperatures

1 hectopascal is equal to 30ft change 
1º celsius is equal to a 120ft change  br>

If you are looking for the landing and T/O I would suggest looking a Performance charts-which