Wrong. Simply raising the the temperature of an object does not raise the mass. What are you guys smoking?
We're smoking Einstein's old pajama pants. Also, we're correct and you aren't. Higher temperature means more energy in a system. More energy means more mass. Yeah, it's a little weird. It's also an inevitable consequence of the constant speed of light, and the conservation of momentum and energy. Starting with those three assumptions you can prove that E=mc^2.
To do the math:
1 kg of Carbon Steel raised 1 degree Kelvin will gain 5.45e-9 grams
Specific heat of Carbon Steel = 490 J/(g*K)
Energy required to raise 1 kg 1 degree K = 490*g*K = 490*1000*1 = 490000 joules (kg*m^2/s^2)
mass of 490000 joules = m = E/c^2 = 490000 kg*m^2/s^2