If it's frozen, and the warm air is deep enough, it melts.
Also, this warmer air may be a good bit drier than the nearly-saturated air whence the precipitation came. If it's dry enough and deep enough, and if the precipitation not particularly intense, it may evaporate before reaching the ground. However, this evaporation will bring down the temperature and increase the humidity of the warm/dry layer of air, so this process is self-limiting in most circumstances.
Convection Precipitation.
Not normally before a warm front, precipitation comes before and after a cold front. When you have warm air and a cold front comes through, you mix warm with cold and that brings precipitation.
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The warm air mass is forced to rise, creating convection and precipitation.
The warm air rises
Precipitation is usually the result of warm air meeting cold air currents.
when warm and warm air meet
When a cold front hits, usually the warm air rises.
A cold front develops, often resulting in precipitation, and sometimes thunderstorms.
Convection Precipitation.
It is the rising air in the center of the low that causes clouds and precipitation (not necessarily warmth though.
Not normally before a warm front, precipitation comes before and after a cold front. When you have warm air and a cold front comes through, you mix warm with cold and that brings precipitation.
rain
The type of front which will lead to turbulent air and precipitation is a cold front. When warm cold air collides with warm air, it will generally produce severe weather.
occluded
A warm air mass catches up to a moving cold air mass, sliding over it.
The warm air mass is forced to rise, creating convection and precipitation.