If your asteroid or comet manages to get broken up into many smaller fragments, but all or most of them still reach the earth, but are small enough to burn up i

If your asteroid or comet manages to get broken up into many smaller fragments, but all or most of them still reach the earth, but are small enough to burn up in the atmosphere before impact, their total energy would still be transmitted via atmospheric entry friction heat, which itself could cause lethal global air temperature increases. They might last only a few minutes or slightly more but (the science on this is a bit ambiguous) we could still be talking about temperatures going up into the hundreds of degrees. No big bang, but still catastrophic for crops, plants, forests, people and atmospheric health.