Hi,
When you run the update process via the Joomla updater, it downloads the install package on our website and installs it.
So it's the exact same as downloading it via the menu My account>My subscriptions yourself and installing it manually.
I would recommend increasing the max upload limit of your php.ini to be able to do that.
If you can't, you can also download the install package on your local computer and extract it there. Then, upload all the files and folders of the extracted package to the tmp folder of your Joomla and run the install from that folder via the Joomla installer and that way, you'll circumvent the upload restriction of your hosting.
The next release is scheduled for this week or next week.