Soni,
  Check the back of your space heater to see what it lists as the maximum electrical requirements (amps, volts, watts) for the heater. 
  Then, get a much shorter extension cord  (e.g. a 6', 10' or 12')  that exceeds the current (amps) requirements by a good margin.  Shorter is better here.  Higher amp ratings are better.  Lower gauge number are better (thicker).

  Longer/thinner extension cords will have higher internal resistance, so the voltage supplied to the heater will end up being lower than it really wants.  The heater will have to draw more current (amps) to make the same amount of heat.  That higher current draw (combined with whatever else might be plugged into that electrical circuit) could be what is tripping the breaker.

Cheers,
Jim

 Thank you Jim and Jake.  Very much!
Soni

The cord you have is safe.  You probably wont need 1500 W unless you get weather below freezing.  You would also be fine with a 6 - 12' 14 G appliance extension cord for $10 at amazon and around the same price most places.

Thank you Bob,  I was just looking in Amazon.  I thought I found a good 9' one but then noticed it says indoors.   ... OK  back to Amazon, 

Soni

I'm a licensed electrician the cord you have is more than suitable for your space heater!!

  wheeew   Thank you Will.  Amazon didnt show anything so spcific as the length and gauge, amps etc I was looking for 

Typically the shorter the cord the better off you are and I would make sure that nothing else is plugged in on that circuit. If it is a dedicated circuit with only one plug on a breaker you wouldn't have any problem with overloading the breaker.

Will,  the outlet I'm using is on a garage exterior wall. Inside the garage are 2 small chest freezers. I could unplug them.  Nothing is going to thaw here tonight

I would unplug the freezers so that there is no extra unnecessary load on that circuit.

Unrolling the cord will not make much of a difference but you do have a significant voltage drop when you use a really long cord I would make the cord the exact length that you need to reach from the plug to the heater. Hope this helps you out!!

Sorry I didn't respond sooner my Uconn huskies are playing a big game against Memphis!!

   GO huskies!
the cord I've been using says 15AWGx36.  very hard to see with a flashlight.   Is that a heavy duty cord?

It's probably 16.  See how many Watts it's rated for.  If you use the heater on one of the 2 lower settings it will be fine.  If I remember correctly, most 16 G cords are rated at 13 Amps so using a heater on high with that cord could cause a fire.

Soni,

Lots of valuable suggestions already!   Especially what rcantor just posted!  Not to be a nitpicker, if I might add the following comments, it may simplify and insure connection to your heater is safe and reliable.

For your intended use and given potential load, I would buy the shortest 12 gage cord you can find.   While your existing cord is fine, at the high setting, voltage drop and consequential current increase may push the breaker!  In all probability, unless it’s an appliance grade separate circuit, it is likely rated at 15 Amps.   As is the residential grade receptacle you are plugging into!

Also, unless you have the proper tools and are handy, I would resist the option of cutting existing cord and installing new ends.  With probable long continuous duty of heater load, ends of the stranded wire in cord really should be soldered prior to connecting to new plug.   I would also confirm rating of circuit breaker and make sure this outlet is not serving other active loads or appliances (you mention freezers).  

Just an electrical contractor’s dos centavos worth. 

Thanks for repeating exactly what I already said!! Solder the connections?? Are you really serious?? Maybe they should just get some spent fuel rods and build a little nuke to keep the greenhouse warm!! If they don't have the capability or the electrical know how of cutting a cord what makes you think they can solder??

LOL  Hey Will  I know how to use a solder iron to punch holes in plastic cups   LOL LOL That's my level of electrical tools

Will,

Geeesh,  my apologies if I stepped on your feelings or plagiarized you.  My bad…. thought I gave credit to valuable suggestions of other posters and only meant to emphasize the solution.  

Solder the connections?? Are you really serious??
Yes indeed, dead serious!    This may be a foreign concept in your parts but, an industry standard in my experience.  Unless a compression type terminal connector is used, soldering or “tinning” ends of stranded cord wire is most common.   In fact, I doubt you would find very few manufactured cords, pig tails, etc. that weren’t “tinned”.

If they don't have the capability or the electrical know how of cutting a cord what makes you think they can solder??
Exactly … !   That’s why I stated….”Also, unless you have the proper tools and are handy, I would resist the option of cutting existing cord and installing new ends”.

Maybe I’m just a wee more nitpicky on the issue of cords,   Too many years’ experience, too many injury reports, worker comp.claims, litigation, blah, blah, and I can tell you "Safety” became a number one priority in my company.  Serious job site injuries do too DIY other trade workers tampering or attempting to fix or modify electrical cords was a huge job site injury issue.  Thanks to OSHA and industry enforcement; miswired cord issue is almost a thing of the past, as you can’t bring a cord on a large job without it being inspected.

Sorry for the rant, this issue probably bores the beejesus out of most forum viewers anyway.  Lets get back to talking figs…..