The answer to this question depends on what type of hair extensions you have.
If you have synthetic hair extensions, you should not use heat on them, as they are not designed to withstand high temperatures. Heat can cause synthetic hair to melt or become deformed, which can ruin the appearance of the extensions.
If you have human hair extensions, you can use heat on them. Even though the hair extensions are not technically your hair, you should still treat them as if they were. I mean after all, they are part of your head now! You should take care to use a heat protectant spray or serum to minimize damage to the hair.
It is also important to use a low to medium heat setting on your styling tools, as high heat can cause damage or even burn the hair.
TIP: Do put your styling tool higher than 350 degrees, and if you have ktips, try not to put any heat on the bonds because it can cause the bond to reset.
You should also be using a mask at least once a week to help repair and prevent damage.
My Favorite products to use are any of The Virtue products, which I will have linked below so you can find what works best for your hair!
Ultimately, it is best to consult the manufacturer's instructions or the advice of a professional stylist to determine the appropriate way to care for your specific type of hair extensions.