Shimla and Amritsar lie at roughly the same latitude (~31°N), but Shimla is significantly cooler because of its much higher elevation:
Temperature drops ~6.5°C per 1,000 m altitude gain (lapse rate). This makes Shimla pleasant in summer (15–25°C) and cold in winter (often below freezing), while Amritsar experiences extreme heat (45°C+) and mild winters.