Non-switching PSU gets quite hot

Hello I have a 1A 12V jack wall PSU that is non switching.
I figured out that is non-switching because it is heavy and big, compared to other 1A 12V PSUs that I have.
I do not think it is regulated, because the output voltage measured with no load is 18v.
It was taken out of an old linksys router.

I am using it to power this https://www.pcengines.ch/alix.htm
The site states that this PC consumes 5W at 12V which is a current of 0.41A

However, the jack wall PSU becomes quite hot after a few dozens of minutes of powering the PC. Then it stays at pretty much this hot temperature, it does not get hotter than that.
The plastic enclosure of the PSU, is quite hot to the touch but you can leave your hand touching it for as long as you want without get burn. I am telling this, as an indication of how hot it becomes, since I do not have a thermometer.

Do you think that there might be a fire problem if I leave the PC on for months?
After a day of continuous operation I do not see any problem, but what about months of operation?

Is it normal for a 1A transformer to operate such hot when 0.41A is drawn out of it?
It may be the rectifier diodes that get hot though...

Hi,

...hard to know. (drill a hole in it to see if it runs cooler - JOKE)

I remember that some of those brick-plug adapters did/do get hot to the touch. Maybe it/that type just dissipate heat through the case/enclosure, which is why they are warm unlike modern ones that don't often feel hot/warm and aren't large and must be SMPS.
If there were a sticker or other markings on the adapter, might be a good idea to search for it online, you never know if it is really 1A at 12V.

If you can place your hand on the case for longer then 5 seconds then its sure to be less then 50 degs C. If its like this in its stable state then I would have thought that it would be OK. One problem you might have is the shape of the current pulses the transformer has to deliver. While the mean current is OK, diodes feeding capacitors have a very peaky shaped waveform which may be leading to the magnetic core being saturated on the peaks, causing extra heating.
With out further analysis I would not send this arrangement into space, but it should do for terrestial use.
Frank