Powering NiChrome wire from battery
The issues you are facing are pure Ohm's Law issues.

First, the coin cells. They have a high ESR, Equivalent Series Resistance (or Internal Resistance). 20 ~ 40 Ω, depending on the load or battery state. Stacking them increases the ESR as well. So from a 3V coin cell like the cr2032 (250 mAh average), and a 8 Ω nichrome wire, we solve for I. I = V / R where R = R-Wire + R-ESR.

0.108 A = 3 V / (20 Ω + 8 Ω)

And since we know the current through the two resistors (current is the same when in series) and the resistance, we can see how much voltage is actually on each, with more Ohm's Law. V = I * R.

2.16 V = 0.108 A * 20 Ω and 0.86 V = 0.108  A * 8 Ω.

2.16 Volts of the 3V available, are wasted inside the coin cell. Only V * I = P .86 V * 0.108 A = 0.09 Watts or 90 MilliWatts of Power are going through the Nichrome Wire. Coin Cells are useless in your application.

Alkaline Primary Batteries, like your typical AA, C, D and 9V have much lower ESR, and can be considered negligible for this purpose. So pure Ohm's Law applies.

0.1875 A = 1.5 V / 8 Ω and 1.125 A = 9 V / 8 Ω

A 1.5V AA battery, at a sixth of a 9V battery's voltage, with the same load resistance, will produce a sixth of the current. But the Power difference is much greater. In Power, that's 0.28 Watts and 10 Watts. While the ESR of the 9V is negligible, it still exists, at likely &lt;= 1 Ω, and while reducing the power going through the wire some, the amount of Power drawn by the load is enough to heat the battery up. 9V batteries are designed for low current draws. Drawing 1+ Amps through it is not ideal.

AA, C, and D can handle this better. Each has less ESR than the smaller, and a higher capacity. Due to the lower voltage, you need to combine a few in series to get the desired current and power draw through the Nichrome Wire.

See How do i find nichrome temperature for specifics on heating and Pulse-powering heavy loads with a coin cell on battery loads.