DIAGNOSIS Yes, it's normal for the exterior, especially the door and handle, to get very hot during high-temperature functions like Air Fry, Broil, or Pizza. The oven cavity gets up to 480°F, and that heat conducts through the triple-pane glass and metal frame.
FIX There's no fix because it's not broken—it's a design characteristic of a powerful countertop oven. Your fix is behavioral: 1) Always use oven mitts or a dry pot holder when opening the door during or immediately after cooking. 2) Be mindful of keeping flammable items (paper towels, wooden utensils, curtains) away from the sides and top of the oven while it's running. 3) Consider the clearance recommendations in (4 inches on all sides) to be a minimum for safety and performance.
IF THAT DIDN'T WORK If the door is getting so hot it's warping, the seal is glowing, or you smell melting plastic, then there's a serious fault. Unplug it immediately and contact Breville support. But general, significant heat on the handle is expected.
HEADS UP This is a key difference from a pop-up toaster or a slow cooker. Teach everyone in the household to treat it like a full-size oven door. The "Cool Touch" door claim refers to the outer layer of the triple-pane window, not the metal handle and frame during extended high-heat cooking.