A front can modify in several ways. Take for example the cold front. The air associated with a cold front is not as cold when it moves closer to the equator (moves into lower latitudes). Why is this? There are several reasons. For one, the sun angle is higher in the lower latitudes. This causes the soil temperatures and ocean temperatures to be warmer in the more equatorward latitudes. As the cold front moves over relatively warm soil or water, the soil or water will conduct heat upwards and modify the cold front (make the cold air less cold). The same is true when someone opens the door on a hot summer day. The heat from outside rushes into the house, making your air conditioned home warmer than you would like it to be.
The depth of the cold air behind a cold front tends to get more shallow as it moves equatorward. The more shallow the cold air is then the quicker it will modify when moving over warm land or water.
A warm front can be modified also. If the warm front moves over cold water or land, the warm air will cool. The land modifies the air above it. This is how air masses form in the first place. If the land cools, it will cool the troposphere. If the land warms it will warm the troposphere.
Another way a front can be modified is through evaporative cooling. This is especially true of a dry air mass. Suppose a cold front moves in and the temperature at sunset is 35 degrees F with a dewpoint of 20 degrees F. Now suppose it rains. The evaporation of precipitation will cool the air. Evaporative cooling causes air behind a cold front to become cooler than it otherwise would be if it did not rain. Cloud cover and lack of cloud cover also modify a front. If the day is sunny, the land will warm and warm the air above it. If it is cloudy, the air will not modify as much and fronts will not modify as quickly. A front is the advection of an airmass away from its source region. Once the air mass leaves its source region, it is vulnerable to being modified. You may well know that the temperatures are colder behind a cold front in North Dakota as compared to Texas. This is because the land gradually warms the cold air as it heads south toward Texas.