I'll check the core tonight -- this is a Presta valve. I don't know where it's leaking. I only put in ~ 70 - 80 PSI (tires are 95 PSI I think).

I don't know if these rims have a PSI limit, but they might be considered somewhat narrow for the 27 x 1 1/4" tires I am using (though the other wheel seems fine) ...

Both wheels look pretty normal with these tires (the tires don't look too wide for the rim).

I may just replace the tube and check the tape to make sure the valve hole doesn't have any rough edges.

It is hotter in this room than in the rest of my apartment, maybe around 80 degrees F.