The default config is in library/Zend/Http/Client.php
Check line 114.
The default is 10 seconds.
If the issue is happening on a constant or regular basis, the solution is definitely not to increase the timeout. You should be troubleshooting with your host why that would be reaching even close to 10 seconds.
Changing it in the core code probably isn't a good idea.
Changing it in the add-on code might be more reasonable - the developer should help you with that. At some point, the add-on will be calling our Http helper or the Zend_Http_Client class - you can specify a timeout in the options array which is passed into that. Doing that would then only affect it for that one thing rather than doing it for everything by default.