The data sheets for nichrome wire indicate that there is a hot ohm specification, as well as a cold ohm spec. Difficult to say what your data is for, without more detail.
It would be worth a try to get some clips, or maybe some crimp type terminal connectors, and see if 120 V and a 6 foot length or your wire would provide a usable heat source .... without any significant problems.
One thing you would want to do is to physically stabilize the nichrome wire when it is in place.
Find some ceramic knobs, or something similar. You could zig-zag the wire, or arrange it in a suitable pattern in front of the ventilation fan, and not worry about it getting out of shape. Ceramic knobs with spikes were available at hardware stores ... and were used for electrical purposes, at one time. Any type of is ceramic insulator might be useful as a support.
Another thought .... If you are not going to be physically lifting your incubator, you could allow for some additional interior volume at the bottom of the unit, and install some extra thermal mass.
Thermal mass might consist of 50 or 100 lbs of ceramic tiles. Rock salt might work as well.
It depends on how much cleaning/sanitizing ... convenience factor ... is going to be required. The extra thermal mass would attenuate .... decrease ... adverse thermal effects that result from opening the access door.
With extra thermal mass, the start up period would be extended until the operating temperature is attained.