When a material is heated its toughness 1. Increases 2. Decreases 3. Remains the same

depends on the material and how you heat it and upto what temperature.

Not much happens with the toughness, but if it passes a critical temperature, the toughness can fully disappear

FI.  steel, it can withstand high temperature, but when it passes its critical temperature it losses all of his toughness.

concrete, it can withstand high temperature, and with the right dimensions not much happens, until you heat it up to the critical temperature of one of its elements. Reinforced concrete is different, the rebar in it is mostly the biggest problem

The most accurate answer

2. Decreases

decreases  like copper,it will become weaker when it expands and its tensile strength is no longer adequate enough.

Heat Treatment involves heating/reheating the material to a certain temperature and then cooling it at desired rate. Heat Treatments are most commonly used in Iron & Steels to get desired properties. Some eg: Hardening: Involves heating the substance to requisite temperature (usually900 deg C and above) and then RAPIDLY COOLING- in water, brine, oil, etc to increase its hardness. 

According to Basic Thermo Theory when A solid is heated the Excitation between the atoms increases and they go apart from each other so the surface area increases and hence the toughness is decreased

Its Toughness decrease because it exapands and spaces has been created beween its particles

Heat treatment on material vary from material to material so its consequences are also vary depending on their molecular structure.

Well, as a direct answer for the question,it is2. Decreases

Decreases with the time at which the material is subjected to the heat, as long as the material is subjected to the heat, as long as the toughness decrease, also the strength of the flame is important factor proportional to how fast and short time the material takes to decrease its toughness

and that is general saying, and for specif sayings, it does depend on the material properties, such as type, its yield strength, Ultimate strength, its Critical points of reaching the toughness, etc

so Just as other answers were,i just add my direct answer to the question, that it does decrease, but dependent to the material properties

Agree with Answer added by: Wolf Klaas Kinsbergen 

I agree with Wolf Klaas Kinsbergen

if a material is heated and then slowly cooled its toughness actually increases.

if it is heated and cooled suddenly it will become brittle

in case of lighting filaments,after heating and cooling the material will remains the same because of its character eg:tungsten