Very hot is subjective. High wattage compact chargers will often get hot. Ideally, they will use components, especially capacitors, that are rated for those temperatures.
If you measure actual temperatures and find them to be above the usual limits for components, then you could contact Framework support & see about a warranty claim.
If you play games that require a lot of power then the laptop will take power from the battery as it is charging implying the charger is already at max output and so will get ‘warm’ ‘hot’.
So do you have a temp for ‘hot’
I have the ‘official’ Framework 60W PSU and an Intel 1167G7 and use Ubuntu 24.04 with no issues. I also run from a small LinkON car-type 12V adapter that provides 65W PD also with no problem.
Has this behavior occurred before or is it just occurring now? Is this the first time you’ve actually touched the charger while it was plugged in before? If it is a lot hotter than before, it could be a hardware issue, otherwise it likely is within what the power supply is rated for.
While I do not have any knowledge of the Framework 13 charger, I can say that when running heavy workloads on my Framework 16 (3D Rendering), the charger sometimes gets so hot you can’t even touch it for more than a few seconds.
The charger likely can get to those temperatures, although of course it definitely isn’t recommended or good for charger longevity.
I would recommend possible putting something to cool it down, such as placing it on a metal surface or even maybe adding an ice pack if you are going to need the constant high performance for a long time. Just make sure no water gets in otherwise both the charger and computer might die.