Thank you all, guys, for your answering and worrying. I'm even that water and high voltage is not a good combination to play with, and I promise I will be careful with this. But, once dealing about sink heater, it's unavoideble... I know too so that using DC, and rellays as switch, it is more simple, safe and apropriated (and was already decided for this way) but, quite so, my problem (doubt) still stays: how to make a thermostat, that uses a thermistor as a sensor, work directly in a 110 VAC, without a properly DC power source device?
Thank you too, Mr. 3vO, for your detaileds and finest concernings, but I'm afraid that they could be a bit expensive to me now (by the way, I did not undestand very well , I'm sorry, what means your last paragraph.
Tank you too, Mr. Ericgibs, I have a basic sink heater already, and all wat I dream with is to adapt in it a thermostat, and this thermostat should work in order to turn the heater charge off when certain temperature was detected inside the tank. And it is irrelevant to me if the thermostat works on or off board, since works. And be sure you are not downbeating me, but instead encouraging.
Anyway, I'm gratefull for you all for your contribution. I apreciated and wil analyse the sugestions (and I hope you, Sceadwian, were better (or more serene, at least...) now, from the shock you got). Forgive me if being boring.
Best Regards
SiriBrazil