Warm or cool water may work, but hot is more effective.
If you use biodegradable dryer sheets, this can be an especially green cleaning solution.
To conserve your baking soda, it’s not necessary to cover every inch of the pan, but give most of it a good covering.
If you don’t have a spray bottle, gently pour water onto the baking soda, mixing it slightly to form a paste on the pan.
Dampen the towels every so often if you feel they are drying out too quickly.
If you leave the pan sitting overnight, most of the water will evaporate, which is okay.
Hot water is not necessary, but warm water is more effective than cold water in cleaning broiler pans.
Bar Keepers Friend also offers a spray which will do the job, as well. Find Bar Keepers Friend in the cleaning supplies section of the grocery or big-box store.
If you only have one sponge, it won’t hurt anything, but rinse the sponge thoroughly after you finish cleaning the broiler pan.