Wire heater from laptop power supply
If you have a supply of 19V with a maximum current of 4A, then the resistance of the heater must be at least 19/4 = 4.75\$\Omega\$.
You need to choose a heating wire that has at least that much resistance. (More resistance if you want lower power. 4A times 19V is 76 Watts. That may be too much for a small hive [I don't know], so you may want less power.)
Do not try to modify the supply so that the over-current feature is disabled. That feature is there to protect the supply from burning out.
Addendum: My understanding is that bees are very sensitive to over-heating. I would strongly consider using a thermostat (or something similar) to prevent accidentally killing off your hive.
The temperature of the wire (as opposed to the total heat generated) will depend upon the current and the resistance per unit length. That in turn depends upon the wire diameter, as well as the conductor material (for example copper vs nichrome). I would recommend a longer, fatter, less resistive per unit length wire, which will not run as hot, rather than a shorter, thinner, high resistance per unit length wire, which will run hotter.