  We present radiation hydrodynamic simulations in which binary planets form by
close encounters in a system of several super-Earth embryos. The embryos are
embedded in a protoplanetary disk consisting of gas and pebbles and evolve in a
region where the disk structure supports convergent migration due to Type I
torques. As the embryos accrete pebbles, they become heated and thus affected
by the thermal torque (Ben\'{i}tez-Llambay et al. 2015) and the hot-trail
effect (Chrenko et al. 2017) which excites orbital eccentricities. Motivated by
findings of Eklund & Masset (2017), we assume the hot-trail effect operates
also vertically and reduces the efficiency of inclination damping. Non-zero
inclinations allow the embryos to become closely packed and also vertically
stirred within the convergence zone. Subsequently, close encounters of two
embryos assisted by the disk gravity can form transient binary planets which
quickly dissolve. Binary planets with a longer lifetime $\sim$$10^{4}$ yr form
in 3-body interactions of a transient pair with one of the remaining embryos.
The separation of binary components generally decreases in subsequent
encounters and due to pebble accretion until the binary merges, forming a giant
planet core. We provide an order-of-magnitude estimate of the expected
occurrence rate of binary planets, yielding one binary planet per
$\simeq$$2$--$5\times10^{4}$ planetary systems. Therefore, although rare, the
binary planets may exist in exoplanetary systems and they should be
systematically searched for.
