The short answer: treat the stains first, then wash on the setting the fibre allows, which is warm for linen and cotton and cool for polyester. The complication is that a tablecloth collects three stains that need three different chemistries. Candle wax needs heat and absorbent paper. Oil and grease need a solvent, because water alone will not shift them. Wine and juice need neither, and heat sets them permanently. And one number matters more than any of it: the iron temperature that melts wax out of linen is close to the temperature that distorts a polyester cloth, which is why the published advice ranges from the lowest setting to a hot iron without saying what the cloth is made of.
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