Can a power station run a space heater?

Yes — and it will flatten the battery faster than almost anything else you can plug in. A 1,500 W heater empties a 1 kWh power station in about 34 minutes.

Drain table (1,500 W heater on full; 750 W on low)

Power stationFull power lastsLow (750 W) lasts
300 Wh10 min0.3 h
500 Wh17 min0.6 h
1,000 Wh34 min1.1 h
2,000 Wh68 min2.3 h
3,600 Wh122 min4.1 h

Includes the 0.85 inverter efficiency factor. Real results vary slightly with battery age and temperature.

Quick answers

Why is electric heat so brutal on batteries?
Resistive heating converts electricity to heat 1:1 — there's no efficiency to find. 1,500 W is 1,500 W, and a 1 kWh battery holds… 1 kWh.
What should I use for heat in an outage instead?
Blankets and layers first; a propane heater rated for indoor use (with ventilation); a diesel heater in vans; or a fuel generator if heating is non-negotiable. Save the battery for fridge, light, and comms.
What about a heated blanket instead?
Much better: 50–100 W instead of 1,500 W. A 1 kWh station runs a heated blanket all night with room to spare.
Size a battery for loads that make sense