Could a planet form without a molten state?

Based on what I know, the Earth accreted out of the solar nebula, had a period when it was entirely molten, and then slowly cooled. Could a planet form without ever passing through a molten phase?

• I don't see how that could be possible; even the slowest collisions between large enough bodies would have enough kinetic energy to produce enough heat to cause thorough melting of the two bodies, and their mutual gravity would cause them to accelerate towards each other thus producing even more kinetic energy and heat. – BillDOe Apr 5 '19 at 19:51

If you accrete a mass of $$M$$ the total binding energy will be $$3GM^2/5R$$, which will at least partially turn into heat. If the melting temperature is $$T$$ and specific heat capacity $$C$$ we get the condition $$\frac{3GM^2}{5R}=CTM,$$ or $$M/R<5CT/3G$$. So if we use a low silicate rock melting point of 600 C and basalt thermal capacity then $$M/R<1.8313\cdot 10^{16}$$ kg/m, while the upper range 1200 C gives $$3.0899\cdot 10^{16}$$ kg/m. So if we consider a basalt planetoid it will start to have some melt when cohering into one ball of radius larger than 1000 km. So, not much of a planet.