Moving tmp folder out of public_html and the Captcha image

Due to me finetuning security measures for my site I have moved the public_html/tmp folder out of public_html.  This caused my registration Captcha to fail (there was no Captcha image on the registration form).  As I don't want to use the reCaptcha, that isn't very user-friendly I need to change the path for the Captcha image writting towards the tmp outside of the public_html.
I created a folder named bbbb outside of the public_html and put the tmp folder inside that.  In the site configuration I changed the path of the tmp folder to the bbbb/tmp outside public_html so the site is working fine except for the Captcha image of Ajaxregistration.

For the time being I created another tmp folder inside public_html just for the Captcha to write in there, but I'm convinced this can only be a temporary measure, because having tmp inside public_html is considered a security issue.  I imagine I should change the path in the ajaxregistration core coding so it will write to the tmp outside of public_html.

Can you help me with this?  Where do I find the path and what modification should I do?

The error message I got when the Captcha image didn't appear because it couldn't find the tmp folder in public_html was:

Warning: imagepng() [function.imagepng]: Unable to open '/home/xxxxxxx/public_html/tmp/captcha_c1849597204.png' for writing: No such file or directory in /home/xxxxxxx/public_html/components/com_ajaxregister/libraries/captcha/captcha.php on line 1312

Well, I hope you understand my problem and can give me some help.

+1

I do also at the same problem.
Solution needed.