That's not good, but hardly fatal and probably to be expected if plain old extension cord was used in the last rewire. As you have probably noticed, these things run hot. Replace with high temperature fixture wire (150 degree C min. 200 degree C rated is better if you can get it. Teflon...
We have a vast forest of very similar lights, some going clear back to the 1930s. Ours were all ether purchased with Med PF (medium prefocus) bulb sockets or have been converted to such. We usually lamp them at 500W with a BTL type bulb. They are not terribly efficient, but they are frequently...
Talcum powder between set pieces. For semi-permanent joints (skin to platform frame), use screws instead of nails (Nails are much more likely to to loose their grip and allow motion to occur. Especially with all of the flexing that stage platforms usually see.) If these platforms are intended to...