I am curious regarding home heating costs.

Let me use the situation, of three identical homes heating with the same central systems.

1st home. The thermostat is left on all the time at 70 F
2nd home. The thermostat is left on all the time at 72 F
3rd home. During the day the thermostat is left at 68 F, and during the rest of the time left at 70 F or 72 F.

Would there be a significant difference in the heating cost over the same period of time? Once the home reaches the desired temperature, is it more costly keeping the home at the higher numbers than lowering & raising at different times of the day?

In the winter, the colder it is inside your home, the less heat you will lose. The warmer your house is, the more heat you will lose. Why is that?

Let's take the scenario of your first house. The inside of the home is kept at 70°F and, for the sake of argument (and simplicity), the temperature outside is always 40°F. The temperature difference is 30°F. The rate that heat is lost is directly and proportionately related to the temperature difference. It doesn't matter what the actual temperature is on the inside, or the outside. Only the temperature difference matters. If we double the temperature difference, we double the heat loss.

We'll keep this simple and ignore drafts and the opening of doors, etc. To keep the house at the same temperature, the furnace must supply heat to the home at the same rate that it is lost.

If we move to the second scenario, the house is being kept at 72°F, and the temperature outside is the same, 40°F. The temperature difference is now 32°F, which is approximately 7% larger than 30°F. Our rate of heat loss is now 7% greater, which means that our furnace must burn 7% more fuel to balance the heat loss.

If we install a setback thermostat and keep the house at 70°F for twelve hours and 68°F for twelve hours, how does that affect heat loss? Obviously, during the 70°F period, the heat loss is the same as the first scenario. During the 68°F period, the heat loss will reduce by 7%. Averaging that over the full 24 hour period yields a net savings of 3.5%.

Obviously, the temperature does not stay constant on the exterior of the home all day long, but this gives you an idea of how this works.

Now, you might wonder if the energy savings make up for the fact that the furnace has to work harder to get the house back up to temperature when the setback thermostat calls for a warmer temperature. The answer is "no." But what does make up for this is the fact that the furnace is not needed at all during the period that the temperature is allowed to drop from 70°F to 68°F. The warm-up and cool-down period cancel each other out in terms of energy consumption. The net effect is that for every hour that you reduce the temperature inside the home (thereby reducing the temperature difference), you will realize save some energy.