Possibility of dissipating 20 W via Nichrome wire safely
Let's try to ball park this to see if it's reasonable to use only 12" of such thin wire dissipating 20W: 

The surface area of your AWG32 wire is \$\pi \cdot \text {(0.008")} \cdot\$12" = 0.3\$\text{in}^2\$, so the watt density is 67W/\$\text{in}^2\$. 

Maximum recommended watt density for vegetable oil with operating temperature of 400°F is 30W\$\text{in}^2\$, and even less for lubricating oils with 250°F operating temperature (more like 13-23W\$\text{in}^2\$) so I would say that you are likely well above the maximum watt density for reliable operation using transformer mineral oil. 

You would be better off using a commercial cartridge heater with a much lower watt density (much more surface area but similar wattage).