Export template doesn't work

A few days ago I've downloaded the Explorer template. Everything works OK but the export function. Just to test if it happens again, I've also installed the Sparky Pro template (my subscription is valid until February 2015) and the export function also doesn't work. I couldn't find any errors in the Joomla error logs, but there is a record in my cPanel (Apache) error log which, maybe, may have something to do with this:
[:error] SoftException in Application.cpp:601: Directory "/home/xxxxxx/public_html/templates" is writeable by group, referer: www.xxxxxx.net/administrator/index.php?o...le&layout=edit&id=12
I'm aware thet there were some problems with Sparky and Joomla 3.2, but they've supposed to be resolved (just to be sure I've downloaded the latest Sparky Pro install), and I'm using the latest J 3.3.6. Of course I can just duplicate the template using the Joomla function, but I'd prefer to have the template working like it should, with the export function.
Since I'm at this, I also found a few lines in the error log concerning mod_hot_full_carousel, although they are not visible in the front or the back end:
PHP Strict Standards: Only variables should be assigned by reference in /home/xxxxxx/public_html/modules/mod_hot_full_carousel/tmpl/default.php on line 13
Can this be fixed or should I just ignore it, since it doesn't affect the functionality, as it seems.
Thank you for your help.

try this, set CHMOD of this folder:

templates\hot_explorer\export\

to 777


Also in joomla global configuration level down 'Error Reporting' parameter so that warnings don't pop out

Thank you for your answer, but...
Changing chmod to 777 doesn't help, export is still not working. At the moment I have error reporting set to "Simple", but this also wasn't the problem - no error message pops out when I try to export the template (even if I set the error reporting to maximum), just nothing is happening when I click on "Export". It would be easier if there was an error message to point me...
On the other hand I have another site on the same VPS using the Sparky Pro template, recently upgraded to Joomla 3.3.6 - so I tried to install the same Explorer template there, and it exports without a glitch. This would mean that no Apache-PHP-MySQL configuration or version could be the cause of this, and the "Export" folder there has a usual chmod 755.
Just to test it, I've exported the Explorer template from this second site, and then installed the exported version to the first site. The exporting function still doesn't work...
I'm a bit confused with this. This is a brand new site that I've started, and apart from installing the Explorer template and the Hot Full Carousel module, I've installed just a few languages (it is a multilang site), Akeeba backup and NoNumber Module manager - all the things that I also have installed on my other sites.

It seems that I have resolved the exporting problem.
I've deleted the complete Joomla instalation, and created the site from the beginning - but this time, instead of using the Softaculous installer (I was trying to save me some work by using it), I've installed Joomla the usual way, uploading the installation file by FTP. This was actually the only difference between the two sites with working and non-working export function, and it seems that this was the problem - since the export function now works OK.
I'm not sure where exactly the problem was, but some time ago I've already encountered some issues (with Joomla update function) when using the Softaculous Joomla installer instead of the regular Joomla installation file.
So I thought I'd share this, if someone encounters the same problem.

Thanks for sharing your expirience