Yes, the colour temperature of the bulb/carbon arc rods, and the screen colour are taken into account when doing a preservation that will be purely digital. These were actually pretty heavily regulated and the values are well known.
It doesn’t have to get to building a collider level of pedantry, but understanding colour science, and the original projection standards vs the colour systems of current digital devices is absolutely essential if you want to approximate the colour of the experience of seeing the print projected.

Brightness, that is an issue, but there were standards for the amount of foot/lamberts that a cinema was meant to have, and good cinemas did adhere to. So in your own home, you can calibrate your system to give a close approximation of the brightness levels that a good cinema would have exhibited.

It is best watched on a projector if you are leaving grain levels as the are on the scan, if you are watching on a television, then the grain will look far, far more pronounced than a projected print would look.
This stuff probably should have its own thread in the technical section, and get discussed there.
Otherwise it can look like people are dissing the efforts of everyone on this project, but it is a valuable discussion to have, and it is all something very much taken into account when companies that care enter into a restoration of their film properties. The film Suspiria that we worked on recently spent weeks discussing colour, grain and dynamic range settings to get the home experience to as closely match the cinematic experience as possible, and a lot of work and research went into it, so it is important, but maybe lets take it out into the other room if we are going to get into the nitty gritty?