burning, fierce (esp. BrE), great, intense, searing, terrible, tremendous
The soil is baked dry by the fierce heat of the sun.

gentle
excess, excessive
If circulation is impaired, the body cannot lose excess heat.

red, white (often figurative)
Everything he did was at white heat and lightning speed.

radiant
body

feel
We could feel the tremendous heat coming from the fire.

disperse, dissipate, give out, lose
Even after the sun had set, the stones continued to give out heat.

conserve, retain
The thick walls retain the heat.

absorb
Darker surfaces absorb heat.

conduct
Being a metal, copper readily conducts heat.

create, generate, give off, produce, provide, radiate
Computers and photocopiers all generate heat of their own.

withstand
a material which can withstand heats of up to 2 000°C

build up, increase
He tried to ignore the heat building up in the confined space.

come from sth, come off sth (esp. AmE), radiate from sth, radiate off sth (esp. AmE)
I could feel the heat coming from the fire.

loss
exhaustion, stress, stroke (usually heatstroke)
She slumped to the ground suffering from heat exhaustion.

heat from
the heat from the fire

baking (esp. BrE), blazing, blistering, boiling, extreme, great, intense, oppressive, scorching, searing, shimmering, stifling, suffocating, sweltering, unbearable
We walked more than ten miles in the blistering heat.

dry
humid, steamy, sultry
the steamy heat of New York in summer

40-degree, 90-degree, etc.
afternoon, midday, morning
summer
desert, tropical

grow
Daily the heat grew.

get to sb
I think the heat is getting to all of us.

haze
A heat haze shimmered above the fields.

wave (usually heatwave)
source

in the heat
I can't work in this heat.

the heat of the day
To avoid the heat of the day we went out in the mornings.

high
gentle, low
medium, moderate
direct
Chocolate should never be melted over direct heat.

dry

turn up
Turn up the heat to caramelize the sugar.

lower, reduce, turn down
remove sth from, take sth off
Bring to the boil slowly, then remove from the heat.

return sth to
Return the pan to the heat and stir.

off the heat
Make sure the pan is off the heat.

on a … heat
Cook on a low heat for five minutes.

over a … heat
Simmer the sauce over a gentle heat.

electric, radiant

have
The house has electric heat.

have on, use
Andy had the heat on full blast in the car.

turn on
They are afraid to turn the heat on because it's so expensive.

turn off
They have their heat turned off during the morning.

turn down, turn up
I turned the heat down several notches.

provide
These industries provide heat for our homes and fuel for our cars.

be on, be on high, be on low
The heat was on but the window was open.
The heat's on low.

be off
come on
go off
Our heat goes off at ten o'clock and comes on again at six.

sudden
He stared at her, sudden heat in his eyes.

flare, flood sth, rise
Heat flooded her cheeks.

in the heat of
in the heat of battle/passion

with heat
‘It was your idea,’ Henry said with heat.

in the heat of the moment
Michael bitterly regretted those angry words, spoken in the heat of the moment.

qualifying, regional (BrE)
dead
Competition was fierce, with a dead heat in one of the races (= with two competitors finishing in exactly the same time).

win
She won her heat.

in a/the heat
He fell in the first heat.