What's the rating of the heater in amperes, or in watts? And what's the operating voltage?
Generally speaking though it's a bad idea to plug a heavy load like an electric heater into a power strip or a surge protector. Those kinds of off-the-shelf devices aren't designed to handle that kind of a power. It's far preferable to have a dedicated outlet for the device. And if that's not possible then plug it directly into a wall outlet. Extension cords are also a bad idea as most are not up to handling that kind of load either. But if you must use one make sure that it's a heavy-duty, appliance-grade cord, like would be used with a window A/C unit, not a "normal" one.
This post was edited by Salt and Red Pepper at November 8, 2016 3:52 PM MST
To add to Salt & Red Pepper's point about extension-leads, you can use one IF its current rating is above that of the heater, is correctly fused or otherwise overload-protected, AND if the reel-type, is fully unwound.
The current capacity of an extension-lead on a reel drops significantly if the cable is left partially wound up. Handling a hefty alternating-current, if left closely coiled it becomes an inductor, and the power this loses is shed by the cable over-heating.
I gotta wonder where these old "wives tales" even come from, let alone why they continue to persist . . .
Reactance of the inductive flavor (or of the capacitive type for that matter) does NOT cause heating. Reactance only "stores" energy. It does NOT dissipate power. Only resistance can do that. Even if that was a factor even a 1,000-foot portable cord (appx. 300-meters) has very minimial inductance/inductive reactance at AC power line frequencies, even when tightly coiled.
The actual possible issue is I2R losses (the current flowing in the conductor, times itself, times the resistance of the wire). Resistance numbers vary, depending on whose data you look at, but a common number given for 12-AWG copper wire is around 0.00158800-ohms/foot (12-AWG is probably the heavist cordage commonly available at your local hardware store in the States, but MUCH heavier is available). For a run length of 250-feet that would be a resistance of about 0.8-ohms (two conductors are involved, the resistance in both directions is additive) For a current flow of, say, 15-amperes that would be a power dissipation of about 180-watts, which is quite a bit (ever touch a 100-watt incandescent light bulb in operation?). That should not be an issue for any "Code-acceptable" portable cordage when unwound and distributed over a flat surface as the heating will be (more, or less) evenly distributed as well. But if it's all wound tightly in multiple layers on a cord reel it's like having a 180-watt electric heater contained within multiple layers of electrical (and thermal ) insulation. That's still not an issue if the insulation on the cordage is properly rated; "reeled" cordage is available in the States with no de-rating in use, coiled vs. unwound. But if it's the cheap PVC "light duty" stuff your're going to be able to roast weenies and marshmallows sooner or later.
Which brings us to the term "appliance grade" for portable cordage. That term has special meaning, more stringent requirements, and it must be demonstrated to meet those requirements. (Although it seems that UL , ETL, CSAus, etc. stickers are easy to print, especially in China). Generally speaking though it refers to relatively short cordage (12-feet or less in length is typical, and the Code sets a maximum length which I don't remember off the top of my head). Such cordage must be able to continuously pass the rated current of the end receptacle (and a single receptacle, not a "Medusa") while exhibiting the characteristic of staying withing a specific temperature rise. They're not your "run-of-the-mill" "light-duty" extension cord. THAT'S why I used that term for any possible extension cordage for a heating "appliance".
I can tell you exactly the source of what you call an "old wive's tale".
It is the manufacturer's warning on the reel itself, carrying a lead 15m long rated at 240V (now 230V) AC and maximum 13A current capacity, and physically perhaps 10 turns wide on a minimum diameter of about 150mm.