I think it will depend on where you are, how cold it gets, what the humidity is, the rainfall you get..
I am concerned that your strawbales will break down and mold, also attract small beasts which you do not want living in it. As someone up above stated, moisture issues may be a problem. If they get damp and start to compost, they can also possibly generate some heat and MAYBE start a fire.
When I built my root cellar in upper B.C., Canada, I looked to what the gold miners and fur trappers in my area did 140 years prior as many of their root cellars were still quite usable if the door had been replaced. They were 100% log and dirt and had stood the test of time. There are so many standing dead trees up there from Mountain Pine Beetle, that is was an easily found and low cost building material for me. I decided time tested was the way to go. What is traditional to build as a root cellar in your area? Why or why did they build them that way? I am not trying to discourage you from your strawbale one, but before you put all that work/time into one....
I couldn't have done just log here in Oregon due to the rainfall and humidity, but when a friend and I were discussing how he ought to build his root cellar in Wisconsin, with his low humidity and water table, I suggested a log one for him as well, since he also had the material free for the taking off his land as well.
If you are building a crawlspace sized one, why don't you do block all the way around for "X" amount of courses or use broken concrete and a slipform wall type on the remaining 3 walls and keep the block for the front? How set are you on the strawbale? Have you gone and visited people/strawbale houses?
I am posting mine cellar pics here to maybe give you some more ideas. I figured since my material was free other than chain saw fuel, the cellar may as well be bigger, so it ended up at 12x17' with just short of a 6 foot ceiling by the time I dumped sand on the floor.
Mine was all log, including the roof, with mill felt over the top and then eventually 24" of dirt. The intake and hot air escape vents were off a single wide trailer. Nothing but the sealer was bought for this project, which ended up to be about $32.00CA. There was some 6" and 8" spikes laying around which is what the roof was attached with on the ends to keep any of the logs from rolling.
The coldest it got outside the root cellar was -45C/-49F and although I did have to cover my spuds up with sleeping bags over the top, they came through just fine in the cellar. I do not remember what the inside temp was, but it was just below freezing. I did used to keep a thermometer and a hygrometer in there.
In hindsight, I would have put electric lights into it and I would have let the soil spill around the sides more instead of holding it back with the extra logs.