Does the metal construct summoned from Summon Construct also cause fire damage when using Slam?

The Summoned Construct’s Heated Body ability is the same wording as the Remorhaz’ (though it does less damage).

Construct Spirit:

Heated Body (Metal Only). A creature that touches the construct or hits it with a melee attack while within 5 feet of it takes 1d10 fire damage.

Remorhaz:

Heated Body. A creature that touches the remorhaz or hits it with a melee attack while within 5 feet of it takes 10 (3d6) fire damage.

but unlike the Remorhaz’ Bite, the construct’s description does not have a clause that it also deals additional (fire) damage on a hit with its Slam.

Construct

Slam. Melee Weapon Attack: your spell attack modifier to hit, reach 5 ft., one target. Hit: 1d8 + 4 + the spell’s level bludgeoning damage.

Remorhaz

Bite. Melee Weapon Attack: +11 to hit, reach 10 ft., one target. Hit: 40 (6d10 + 7) piercing damage plus 10 (3d6) fire damage. If the target is a creature, it is grappled (escape DC 17). Until this grapple ends, the target is restrained, and the remorhaz can’t bite another target.

Does a creature count as touching the construct (and get fire damage) if they are hit by its slam attack?


Info on the Summoned Construct is from Tasha’s Cauldron of everything. Info on Rhemoraz is from Monster Manual