determine which metal would heat up faster, Au or Fe, when 250.0 J of heat were absorbed by the metal

The heat absorbed depends upon the specific heat of any material

The specific heat is the amount of heat absorbed by any material when one gram of a substance is heated by 1 degree celsius

the specific heat of

a) Au : 0.129 J/g 0C

b) Fe : 0.450 J/g 0C

if 250 J of heat is given

then

Heat = mass X specific heat X change of temperature

Change of temperature = heat / mass X specific heat

For same mass and same heat the change in temperature is inversely proportional to specific heat

Here gold will observed more change in temperature or will get more heat up