Template design pattern for operations with parameters

Template design pattern lets you design an algorithm which can be customized by overriding some template methods.

class Algorithm {
    protected void init();
    protected void prepareCup();
    protected TeaBag prepareTeaBag();
    protected void boilWater();
    protected void putWaterIntoCup();
}

prepareTeaBag() can return arbitrary tea bags to make custom tea.

But what if I have an algorithm that would require some parameters for operations, for example name of the tea bag, and some other properties that are being changed into each of the operation. I can save those properties into class as a class members but that way I can't call it from different threads. I would need to pass some Context class that would change depending on operation in order to allow multi threading access, or something what are your thoughts on this?