To ship painting pieces, it's essential to plan properly and to choose a company with solid shipping experience. Paintings are easily affected by the heat and vibration of standard shipping practices and must be treated differently.
In order to ship painting pieces safely, it's important to choose the right shipping materials and use professional techniques to avoid potential damage to the pieces. Modern shipping companies will ship a painting differently depending on its individual features--paintings in frames, for instance, often require different padding than paintings shipped separately from their frames. Reputable companies often use specially fitted foam products to ship painting pieces, as foam doesn't allow heat to build up yet provides sufficient physical protection. There are other materials specially designed to ship painting pieces safely, but standard packaging like bubble wrap and packing peanuts will not protect expensive art pieces and can be dangerous to use.
Always use a shipping company that has experience with paintings and fine art. Experienced companies are more likely to provide insurance and less likely to use materials that could potentially result in costly damage to a valuable art piece during shipping.