Aleph J illustrated build guide

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@Nikko03, in your first picture you show a cover for the transformer with the bolt through the top. Is this electrically isolated from the case? If not, you could be creating a shorted turn through the cover.

Your transformer does look small for the job but you should make sure you aren't creating a shorted turn as well - try unbolting it from the case and see if the temperatures are much different on the transformer. What I mean by this is - remove the bolt and cap from the transformer (unsecured so don't move the amp around) and see if it makes a difference.
 
Transformers typically will be spec’d with a temperature rise at rated power. For some it is 50c and others 70c. Note that it is rated in VA not watts. My Aleph J runs about 270va but is biased a little hotter than normal. If you are running 250va and your transformer is rated for a 50c rise at rated output then 250/300 X 50 =41.7C + ambient temp in chassis of at least 25c an you are right where the specs would predict for transformer temperature.
I am running a 400va in mine and it gets quite warm at 270va but not near 60+ c.
If you are uncomfortable with the temp then you could add a small slow running fan to cool it. You should also make sure there is free ventilation from the bottom of the chassis and out the top cover. This can be encouraged by using high feet and making sure there is room around the amp and above it for air flow. A ZENMOD type babysitter fan would also help by lowering the temp of the entire chassis.
As a rule of thumb I like to stay somewhere in the 70-80% of the rating for a maximum. I am currently using an Antek 20v 400va and it is dead quiet mechanically and not running hot, so I am considering turning up my bias a bit, given that my heatsinks are up to the extra heat.
Check with the manufacturer of your transformer and ask them specifically if the temperatures you are seeing are ok. That will give you peace of mind going forward.