No, do not plug a space heater into an extension cord or power strip.

The U.S. Fire Administration says to plug a portable space heater directly into a wall outlet. Do not use an extension cord or power strip with it.

Why the connection matters

Portable heaters draw substantial electrical power. An extension cord or power strip that is unsuitable, damaged, or overloaded can overheat. The USFA also advises not to plug another appliance into the same circuit as the heater because the circuit may overheat.

Check the heater plug, outlet, and cord for damage before each use. Do not use a heater with a cracked cord, broken plug, loose connection, or a plug that becomes unusually hot. Have electrical problems checked by a qualified electrician.

Place the heater carefully

Set the heater on a solid, level surface. The USFA advises keeping it at least three feet from anything that can burn, including bedding, curtains, furniture, and clothing. Keep the heater and its cord out of walkways where they can be knocked over or damaged.

Follow the heater's own manual for placement, ventilation, and shutoff instructions. Turn it off when leaving the room or going to sleep. Never use a cooking appliance as a substitute for a heater.

Scope

This page summarizes U.S. Fire Administration guidance for portable space heaters. Electrical codes and product requirements vary by country. If the only available outlet is far away, use a safer heating arrangement rather than adding an extension cord.