In the fan speed resistor module there is an overtemp switch that can get dirty. There are two of these on a 944 but I think only one on a 968. This gadget is on the LH side (LHD driver's side) in the air intake for the HVAC system. The overtemp switch looks like a small reed switch or relay.
I have cleaned these little guys with some paper and a drop of acid, followed by a good bath. It's important to get the contacts apart so the inner surface gets cleaned.
I have also had my fan control switch in the Climate Control head break to cause this same problem of only high-speed fan. I replaced my fan switch with one from a scrap CC head. If you decide to replace, the 968 and 944 CC heads from 87 or 88 are much improved, much smaller, more integrated electronics than the 85.5-86 ones (not sure about the dates.) All I know are some of the scrap ones I got were super bulky and stone-age looking.
The 968 also uses a detent pot for the temp control, so if you grab a late 944 CC head that might not be the same.
Cheers,
-Joel.