Red Earred Slider Questions?

  i have a red earred slider and my room stay cold and i have a light over the to keep it warm but its not working so would he be alright in the water that way
it is okay for the water to be

cold but cant be at freezing water tempeture.

under 20 degrees is not good.but above is ok
The turtle can tolerate room temperature water but will not thrive under those conditions. Get an aquarium heater and basking light (s).