You will be safer to use the heavy duty cord and try to run it as short as possible. The problem here is that there is voltage drop with every foot of extension cord that you run, and if the heater has to run a good while, you run the risk of over heating and starting a fire.
I know a lot of people here say you can do it, but, I am a little different. If I was home and running it, it would be a different story, because I could keep a close eye on it, and feel the cord once in awhile to see if it's getting hot. I would NEVER go out of town for a weekend and let it run. I would first try to find someone to come over a few times a day to water for you.
My wife is a burn nurse, and it is very, very sad to see the number of people that are mamed or die each year from using extension cords for heaters. Even though you will not be home to be injured, the risk is there that you could possibly lose everything you have.
The question is: Are you willing to risk it because folks here have not had any problems, yet? That is an answer that only you and your family can come up with. It really saddens me everytime my wife comes home and tells me that a young child died last night in a fire, or that they lost everything because they didn't head the warnings and thought it would be ok.
I know it's a hard decision, but it can also be one of the most important decisions you will ever make.
Good luck.