programmatic secondary structure prediction for >36-mer DNA oligonucleotides
If you really insisted on using Primer3 you could perform a 36bp sliding window analysis. You would submit your primers in 36bp 'chunks' with a step size of say 3 bp. You would need to "circularise" your primer within the sliding window to assess the "beginning" and the "end" and remove "artifactual" hairpins. Its doable via a script and you would automate the web upload and data extraction via a "digger/spider" or else just use a download equivalent (I've used a standalone). There would be a "blindspot" using this approach, which you could overcome if you wanted. 

So summary, its complicated and I think your suggestion of using UNAFold is a better idea.