The smart answer: it can start a fire, don’t do it.

The honest answer: I’ve done it a zillion times and never started a fire. I buy heavy 12 and 10 gauge cords and only chain them to power things that don’t require a lot of amps, like LED lights.

When in doubt, a plug-in power meter is an option you can use to help monitor the situation. Plugs that draw a lot of amps can get warm, even when not using an extension cord. Also, it’s not uncommon for a device to pull a lot of amps on initial power-up, and then settle down to a lower draw.