I picked up a 2001 in January. I drove it from UT to CA and the temp remained low on the gauge the entire drive. I knew I was going to have to address it. I replaced the temperature sensor, the thermostat and the thermostat housing pipe connected to the thermostat all at once. It was my first time doing it. The coolant made a mess, as I expected, but it addressed my problem. I had read the thermostat can often get stuck open or closed. In my case it was likely stuck open. I followed a couple tips I had found online to replace the plastic thermostat housing with a metal one. It also correctly suggested I be sure to get a spare dipstick, as that assembly can easily break while you’re working in that area of the motor. One video I watched suggested I needed to remove several other parts to get to the bolts at the base of the pipe leading to the thermostat. With the right tools I didn’t have to remove but a few items. By right tools, a ratchet with a 2-way pivoting head as well as a ratchet extension allowed me to get to the bolts on either side of the thermostat housing without issue. Thermostat and sensor both work great now. As far as the coolant, I had a catch bin, but it wasn’t big enough. Fortunately I had a tarp down to catch everything so it didn’t flow on the floor.
For my 2001, I found these to be the parts I needed:
Coolant Temperature Sensor - 059919501AKT2 VW/Audi -
https://www.ecstuning.com/b-genuine-...059919501akt2/Thermostat Replacement with Thermostat Housing -
https://www.ecstuning.com/b-assemble...660ecs01-01kt/
Dipstick funnel (commonly breaks when you replace the thermostat):
https://www.ecstuning.com/b-assemble.../06a115611q-1/
With all that said, if you’re running hot, which is the opposite of my issue, you may have a different problem where your radiator isn’t cooling the engine effectively.