Does cutting LED strips into smaller strips then wiring with low AWG decrease temperature?
Yes this can help if done right. Part of the problem with led strips is that a  large roll of flexible printed circuit is used to carry more current than it really should be. This results in a larger voltage droop as you go down the line, ie higher resistance and higher wasted energy, which also has the side effect of making one end dimmer. FPC is fairly high resistance depending on it's cross section. Cheap led strips will cheap out on the copper.

The section of copper that's closest to the power supply will be carrying all the current, ergo getting hotter too. This temperature can affect the leds, which would then draw more current, getting hotter, which means they draw more current. It's called thermal runaway.

But to be honest the heat from the copper is unlikely to affect the leds too much, and with current regulation, like the resistors, which will drop more voltage as the current increases, it balances out.

Cutting the roll into smaller pieces is typically done to prevent the color dimming, by letting the FPC carry less current and the added wire carry the rest. Typically you inject power every 2.5 or 5 meters. So a 10m section would get power injected at 0, 2.5, 5, 7.5, 10 meters. This would be like what you drew in the second picture.

If you really want to lower the temperature, to increase the led life, then you need to either reduce the input voltage, or use a driver to PWM the strip to 80% or lower. This will increase the life of the leds considerably.