The AMD tech specs for XPs gives a max thermal die temp of 90 C. But I think most people would agree that an XP wouldn't last long if allowed to run near this temp.
63 C is a bit high, but probably won't damage the CPU in the short term. In the long term, it may decrease the life of the processor. I have my BIOS set to auto-shutoff at 60 C, but its never reached this high. Of course, lower is better, and I think most people should shoot for sub 50 C temps on the core under load. But then, I'm in San Jose, CA and we keep the room temps at more like 25 C. A 37 C room temp will make it more difficult (and just less comfortable for you too; sorry dude that's crazy hot)
Since the temps decrease when you open the case, it's a good bet that you could benefit some by getting better airflow through the case. My advice is to try and get better case fan(s), heatsink/fan and maybe some arctic silver thermal compound to go with it (can't hurt). If that doesn't reduce the temp much, then I would just live with it. If you can stand the heat, probably the AthlonXP will survive as well