I'm having a weird occurrence. When turning on my gas stove and running for about 45 minutes, my hot water baseboard heat also gets hot.

The thermostat is completely disconnected, yet my heat is on when running my gas stove for long periods.

Any idea why this might be happening?

My first thought is that that is not possible, but then anything is possible.
Why is thermostat disconnected? Is thermostat a low voltage thermostat or a line voltage thermostat?
By stove running do you mean you are using the oven? Are there any exhaust or circulation fans involved?

Has any electrical work been done in your home recently? Turn off gas valve to boiler and see what happens. You will have to relight pilot light.