I have a Sony Vaio SVS13, which I bought in Jan 2013. It looks exactly the same. I have been using it for 6 years now, and in general it performed well.
https://www.notebookcheck.net/Review-Sony-Vaio-SV-S13A1Z9E-S-Notebook.77880.0.html
The fan issue is the same. Even when idle, the fan is always on, in moderate settings, the fan is moderately loud. If I switch it to "Performance" mode, the fan is terrilby loud, and disturbing. Repasting did not help, it is just loud. It's funny to see that even after six years it has the same problem.
My unit also had a design issue: the keyboard touches the screen when the laptop is closed, and make a grid pattern visible from fat. Also, the palm rest is a bit higher, and made a visible dent (scratch) in the screen early on.
I wonder weather they have corrected this issue in the current machine.
Although, over the years I have upgraded the ram to 12 GB (max), I have swapped the HDD to an SSD, and eventually also replace the Blue-ray drive to an SSD (in an enclosure). I am using already the third internal battery, and I have bought a new keyboard this year on aliexpress. I have also replaced the wifi card to a better model. The audio is not working anymore due to a problem introduced in the repasting (done by a professional repair service).
My unit had some limitations, like it did support two screens, but one was the laptop screen, it could only support one external screen, even with the docking station (it was a shock to discover).
I love the "Stamina" button to quicly raisy the CPU speed, and the dedicated "Vaio" button to launch the Vaio app.