1996 Toyota Camry Rattle in rear especially when climate is

First I would check if it is your exhaust system. It could be a rusted off heat shield, a broken hanger or something loose internally in the exhaust system.

If that is not the case and it's more of a suspension clunk, look at your struts, stabilizer bar endlinks and bushings, things of that nature.

Goodluck.

I would have to concur that if you are experiencing a rattle from the rear of the vehicle it is probably exhaust related. Check the exhaust hanger, heat shields. Also if you have a rubber mallet, raise the vehicle and hit the catalytic converter with the mallet. If you here something rattling in the exhaust you have a failed catalytic converter. Often times these will break apart internally and cause rattling in the vehicle.

I just had the same problem with my 1996 Camry, the sway bar bushings were shot. I had them replaced and no mor noise.