E39 Transmission Problem?

[C-Note]

My 1997 E39 has just developed a shaking when driving around town at lower speeds (5-20mph). The temps just dropped to below freezing here, so I thought maybe the fluids were low or completely gelled? It also shakes when braking (not the brakes though) at lower speeds - and will occassionally make a high pitched clinking sound (just in the last day or two). This E39 has 142,000 miles on it, and to my knowledge has never had any transmission issues (I've owned since 53K)

I have seen where changing the fluids may solve many of these issues - but any other ideas? The tranny seems to shift very smoothly and doesn't slip - or maybe it does and that is what is causing the issues with the shaking?

FYI - about a week ago had a rear passenger side tire blowout. Changed to fullsize spare. Other posts have suggested this can cause computer issues - since then (this morning) put all new rubber all around. Took battery cable off for an hour and reconnected - same problem still with the shaking after restart and test drive. Help!

[bad man working]

I don't think this is your gearbox, did this start when you first fitted the spare and did you fit the new rubber to the spare rim ie is the rim buckeled. I think the ATF (auotmatic transmissiion fluid) is lift time in this vehicle and dosen't need changeing it will say on the gearbox sump

[C-Note]

Yes, this started very soon after putting the spare on. However, I just put all new tires on all four normal BBS OE wheels this morning (needed to anyway) and put the spare back in the trunk (spare is full size BBS OE wheel - not bent that I can tell). Tires were mounted and balanced at the tire dealer.