I would like to warm a glass jar to 27°C and maintain this temperature using a miniature digital thermostat.
A thermostat implies an on/off control rather than a proportional control. The thermostat will have hysteresis (usually 0.5 to 2° difference between turn-off and turn-on points. This will affect the tolerance (which you haven't specified) of how tightly you can control the temperature.
The thermostat is 12V DC and will support up to a 12V 10A load.
That means you can switch power of up to 12 x 10 = 120 W.
Ideally the wire would not go over a temperature of 27°C.
The wire will have to go over 27° to bring the jar to 27° in any reasonable time.
The jar will be covered in material so I can't flash warm it with on/off bursts of heat. More of a constant warming.
The jar will have a thermal time constant. Bursts of heat in the order of 1/10 of that time constant will be smoothed out by the thermal inertia of the jar. This is standard industrial temperature control.
Resistance: 2.02 ohm/M.
Resistance: 2.02 Ω/m. (Note small m for meter.)
I would like to keep my wire usage under 4m per jar.
That means 8 Ω if used as one continuous length. We can calculate the power possible as \$ P = \frac {V^2}{ R} = \frac {12^2}{8} = 18\ \mathrm W \$.
Is that enough? We don't know as you haven't given us thermal loss measurement.
You can calculate the heat loss rate by putting a known power into the jar continuously and measure the ΔT that it stabilises at. e.g., If you put 12 W in and the jar stabilises at 37°C with ambient at 21°C then you can calculate your thermal losses as \$ \frac {P}{\Delta T} = \frac {12}{37-21} = 0.75\ \mathrm{W/K} \$ (watt/kelvin). You could then use this a basis for calculating the power required to maintain temperature from any ambient temperature. I would then double that power requirement to ensure that the jar gets from cold to working temperature within a reasonable time.
Usually a PI or PID control loop is required if you wish for fine control and to be able to minimise overshoot.
You haven't asked an actual question. Please edit your post to clarify where you are stuck.