Well, I've seen the inside of those and I really don't think there is an adjustment in there that would suit your purpose...it's just a spring that gets tighter with heat...and that tension opens the butterfly valve...or vise versa.
That little green loop in the lower right is probably what is yanked to open the butterfly...you might be able to add a manual choke kit once you get that cover off...and the kits actually come with a cover (some of them do) so you can control it a bit better...
If the unit is not functioning properly...replacing it with a manual or OEM parts might be your best bet...
However, hush my mouth, if you find out otherwise be sure to post your findings if you can...always nice to know these things for future reference...