When I accelerate, my air stops blowing cold. Foot off gas pedal it blows cold again.

As the title states, when i'm cruising along at a steady speed, my air is just fine, but if I get on it a little, my air stops blowing cold and just blows warm or less cooler air. I have recently replaced some vacuum lines and my air is working fairly well except this issue. I have searched some of the Air Conditioner posts and it's like finding a needle in the haystack if it's not mentioned in the title. This has been going on for some time and I just realized that the lack of cold air is related to the gas pedal. I would appreciate any help from experience. Thanks in advance. Mike