
Dormant season only like every oak — it is in the white oak group so the oak wilt risk is lower than red or pin oak, but Indiana's April-through-July rule still applies. The species-specific issue is scale: bur oak builds massive, low, near-horizontal scaffold limbs very early, so structural pruning has to happen while the tree is young; correcting a low limb on a mature bur oak means a dinner-plate wound on a species whose thick corky bark seals slowly.
Bur oak declines slowly and rarely from anything species-specific, so when one thins out, look at the root zone first — it usually means fill, trenching, or compaction rather than a pathogen. The two named disorders worth ruling out are bur oak blight, a Tubakia fungus producing purple-brown wedge-shaped lesions along the leaf veins in late summer with dead leaves clinging into winter (documented in isolated Midwest locations including Illinois, not widespread), and bacterial leaf scorch, which browns leaf margins and returns worse every year with no cure.