You have to drop the comnplete rear subframe with the gas tank to remove the rear diff BUT why exactly do you want to do that? Just because it got hot and smells burnt?
A main problem with Volvos older AWD system (not Haldex) is that there's more power robbing and heat buildup in the units than there should be so both front angle gear (bevel gear) assemblies and rear diffs can get hotter than they should and as the fluid expands, it'll spew out the vents. Diff fluid usually smells burnt btw.
If you have mismatched tires, you'll damage one or another costly AWD part as reported here many times before.
If the rear diff isn't noisy, I wouldn't consider replacing it. Now......if you want that car to go fast and don't REALLY need AWD, remove the driveshaft from the angle gear to the rear diff and see if the rear diff still has overheating problems (probably not) and it'll drive normally except not AWD, just FWD.
The rear diff in the car is a pain to replace and costly so I wouldn't advise replacing it yourself unless you have no other choices. It'll require a hoist and trans jack with an attachment to support the gas tank and rear subframe assembly all at the same time, not a job for someone w/o experience IMHO.