How Does caffeine affect bean plant growth?

Minerals like potassium are often found alongside caffeine when it occurs in plant sources like coffee beans, and that could help the plant grow faster. But the caffeine itself would be unlikely to...

I belived that givng caffeine to a plant will cause i it to have no reaction to the caffeine

Bean plants are plants and require sunlight in order to photosynthesise. A lack of sunlight will cause the plant to grow taller in search of sunlight if it receives water but it will yellow in colour.

It does if you put it in the plant.

the warmer it is the faster it grows