Heat styling tools can be used to straighten weaves that are natural wave or straight. As long as everything is performed correctly, you will not see a lot of negative effects as a result. However, in terms of curly and wavy weaves, it should be noted that these kinds of tools should not be used excessively due to the fact that these weaves have already been placed through enough stress in order to achieve their specific styles.
If heat needs to be used to style hair, be sure to use some kind of leave-in conditioner first, as well as a heat protector. This will help prevent any kind of damage to your hair, such as frizz and dryness. However, you should never use a heat protection product that contains any alcohol, as this will significantly dry out your hair.