yes there is, as you are attaching the Heatsink to the heat spreader.
alone heatspreader cannot minimize heat, and for it you require a FAN,
and where there is a contact between two surfaces, you'll obviously require a thermal material/paste
its a very long topic, a if you are interested, then start a new thread with Topic Header, (HOW THERMAL MATERiAL WORKS), and I'll walk you through it in laymans terms.
but for now, for your this query, you need thermal paste regardless of weather ur CPU has a DIE or NOT.
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