Will a planet's core always be very hot? Including formed &amp; forming planets, will the core of a planet always be very hot, or are there any planets with cold cores?
We would expect all large bodies, such as planets, to have a hot interior.

The interior of a planet is heated through two main mechanisms: Heat released from gravitational energy as the planet is forms, and heat released from the decay of radioactive elements, particularly uranium.

The outer layers of the planet are a very good insulator, so the any heat is trapped in the interior for a long time. 

In gas giants, gravitational energy is the main source of heat, Saturn has an internal temperature of about 21000°C, Jupiter is higher, 35000°C in some models. Terrestrial planet's cores are heated by radioactive decay. Earth has a core temperature of about 6000°C. Smaller bodies have cooler temperatures. Dwarf planet Pluto may have a core temperature less than 1000°C, and asteroids would have reached thermal equilibrium, and have roughly the same temperature throughout. 

No planet in the universe can be much more than about 10 billion years old, and this is not old enough for a planet like the Earth to have formed a completely cold core.