You need an incandescent or halogen lamp to provide enough heat.
There are metallic heat elements that are more reliable.
Depending on the size of the tub, 25 watts may not generate enough heat. Most of the small Styrofoam incubators use a 40 watt element and they are much better than a box or plastic for retaining heat. Using plastic, depending on size, you may need as much as 100 watts.
Plastic conducts heat so likely won't have enough insulation to keep the light from constantly cycling. You could wrap it with something insulative like bubble wrap, a blanket or towels.