The weight of a sample of matter depends on its total mass energy, and heat contributes to that total. If matter is cooled, it will weigh less, and vice-versa; if it is heated it will weigh more.

At the kinds of temperatures that normally exist on Earth, the thermal contribution to the total mass energy of a sample of matter is trivial, but in extremely hot conditions, like the first fractions of a second after the big bang, the situation is reversed.