The reason why Black Crusade does not have a rule concerning Unnatural Strength multipliers is simple. There are no Unnatural Strength multipliers in Black Crusade. This was done away with in that ruleset, instead Unnatural Strength (and other Unnatural Characteristics in the ruleset) simply add a set number of additional characteristic bonus points as outlined on page 144 of the Black Crusade rulebook. Example: Space Marines in Black Crusade and Only War recieve a +4 to their Strength and Toughness Bonuses as a result of having Unnatural Strength (4).
In Black Crusade, Page 163 we have the following:
Chainfist entry, 2nd to last sentance, "This weapon double’s the user’s Strength Bonus."
Powerfist entry, 2nd to last sentance, "This weapon doubles the user’s Strength Bonus."
So when you boil it down, the power/chainfists in Black Crusade function identically to those in Deathwatch as outlined above. The only thing which differs is how Unnatural Characteristics work, specifically via multipliers.
RAI and RAW are in agreement on this issue. When you apply a multiplier to an existing multiplier in Deathwatch, you ALWAYS ONLY add 1 to said multiplier as outlined in the Unnatural Characteristics rules in DW:C, and supported by numerous rulings by the FFG folks. For instance if you have 2 abilities you can use at the same time which state, "double your movement speed," you DO NOT get x4 move speed ( MS*2*2). You ONLY get x3 (MS*(2+1)). The same applies to the power fist, this is a UNIVERSAL rule in Deathwatch.
As I stated earlier though, the Thunderhammer only gets the +1 US on damage rolls. On the other hand, you can use the +1 US from the power/chainfist for anything you use that arm for. Climbing, grappling a target, prying open a door, opposed strength tests, lifting things, etc.; the extra US makes any Strength test 1 degree easier (essentially +10 to the roll) and gives more bonus DoS on opposed rolls*. Do not belittle the amazing versatility of such a tool, while the thunderhammer is only good at hitting things, the powerfist can be used for all sorts of stuff.
*Of course, if wearing 1 powerfist on one arm it cannot be combined with special rules of the other arm (+10 to strength tests from high quality bionics for instance). This is both for balance and naturally, the higher US level is already more powerful than the other bonus could hope to add to.
Also, while no official rules govern the use of a weapon in a powerfist the following are good guidelines, though I would still discourage it personally.
1: Attacks with the weapon suffer -30 to hit unless the weapon was designed for an Enourmous character.
2: The weapon uses its normal stats for damage. I.e. a weapon that does 1d10+2 pen 2 will still only do 1d10+2 pen 2.
3: The weapon does not gain the power field rule if it does not have it already.
4: The weapon gains the Unwieldy trait, and loses the Balanced or Unbalanced trait if it normally possesses either one.
5: The Attacker's Strength Bonus counts the same as if making attacks with the Powerfist (i.e. SB x3 for space marines).
6: The weapon may be destroyed from being used with more force than it was designed to use, on a jam (96+ natural to hit) the weapon is destroyed.