Yes, they did, but there was a good extraction system, which you can see in the pic, to remove the fumes from the carbon arcs. This helped to keep the temperature down.
The Ritz was by the market next to the multi storey carpark behind Argos Now been demolished and now just a wasteland If you know where the Firemans Arms is that used to be at the back end of the Ritz
Is the ritz the one that turned into a rollerskate place and is a furniture shop now by birkenhead park?
No, that was the Gaumont. The Ritz became the Essoldo Cinema, then Bingo Club then Top Rank Bingo and closed when the new Top Rank opened. The building was demolished for no reason following a protest and an attempt to have it spot listed. (English Heritage turned down the request as there was too little of the original interior remaining.
Worked at what was the Gaumont about 10 years ago, last time I was in there it was pretty eerie as all the seats in the top deck were still there, some still with residual fire damage, never got to see what was the projection room but when it was Roller World a lot of the area was unchanged, on either side of the stairs leading upstairs it still had "Circle" lighting. The cellars were terrifying, it looked like some funfair that'd gone wrong!
Pics of the Gaumont, opened May 1938, Park Rd. East. From 'The Silver Screens of Wirral', 1989. Essential if you're interested in local cinema history!