The BMW part is a Bypass style thermostat with jiggle pin., 82°C or 89°C, Flange: 48mm, Foot: 27.7mm, Height: 35mm

I don't think that the jiggle pin is important.
A 1994 Toyota Corolla thermostat (fits all Corollas between 1983 to 2001 and 1.3L to 1.8L capacity) will work. Also, the original BMW is unit is 30mm high and the Corolla is 35mm. This is not an issue because when the stem closes the by-pass the assembly pushes against the spring which has a lot of give by design. There are two temperatures, one 82 °C and the other 89 °C. Experience shows that the 82 °C keeps the water and oil temps steady.
Australian manufacturer: Tridon TT214-180 fits many, many toyota vehicles including the following: 4runner, Avante, Camry, Celica, Corolla, Corona, Dyna, Estima, Hi-Ace, Hi-Lux, Lite-Ace, Mr2, Rav4, Soarer, Starlet, Supra, Tarago, Tercel, Townace.

For the o-ring you will need see:
http://www.nak.com.au/products/bs1chart.htmlFor O-rings, you'll want is BS134
Designation Inside (mm) Inside (“) Outside (mm) Outside (“) Section (mm) Section (“)
BS134 47,30 1.7/8" (1.862”) 53 2.1/16" 2.62 3/32” (0.103")
1 7/8” by 3/32” or 47.30mm by 2.62 Grainger #
Tridon TTG47 gasket
Canadian manufacturer: Canadian Tire sells the replacement thermostat and gasket. The thermostat part number is 7214-180 J/V. It is a 180°F (82°C) Failsafe design that fails open should the thermostat break:

The corresponding thermostat gasket is Part number 17-4250-2
