Was the fire kept burning or was it put out during Sabbath? https://biblehub.com/interlinear/exodus/35-3.htm
You shall not kindle fire in any of your dwelling places on the Sabbath day."
First of all, only the Karaites forbid leaving a flame already burning.
Second, this is a commandment that applies only outside the Temple. The commands to bring the sacrifices and keep the menorah burning are explicit in the Torah and thus apply on the Sabbath as well. The menorah is relit every night and left burning until the following night (even Friday night - the Sabbath). There is an explicit command to maintain the fire on the altar all day, from the time it must be rekindled every morning until all the sacrifices have been burned.