Car shakes as if tires are out of balance but only after the car warms up so after five to ten min car starts shaking while excelerating until a certain speed around forty mph what might be the causes

Hello, it's difficult to determine from the words alone what is going on here. If I had to guess, I would be thinking about transmission related concerns or engine misfire concerns which are related to possibly the state of engine condition as far as temperature and all the related sensors providing information as to how the engine should perform. It's difficult to determine, however, a factory trained technician with skills and abilities as well as the proper diagnostic tools and workshop manuals for reference should be able to figure this out pretty easily, with some hands on opportunity to evaluate your vehicle. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops