No sooner had she picked the phone up than she heard Mr Jones' voice icily asking her to go to his office.

icily 是形容词 icy（冰冷的）加上副词后缀 -ly 构成的副词形式。icy 来自名词 ice（冰），形容像冰一样寒冷的状态。icily 在这里形容说话的语气"冰冷、冷淡"，带有不友善的态度。