The BJ-3 doesn't formally enter service until 3042; before that there's just experimentation, per TR 3039 (not surprising, as breaking in new tech must have taken quite a long time; IO lists freezers as only entering produciton in 3040, so this all lines up).
Checking with the MUL, I find that yes that is what the MUL says. But unless there was a deliberate retcon, the MUL may be in error:
The BJ-3 was introduced and named in
BattlePack: Fourth Succession War where it is described (p. 38, New 'Mechs: BJ-3
Blackjack) as having two PPCs, 4 M-Lasers, and according to the fluff text on the same page it was an upgrade ordered by Duchess Candance Liao "after the rediscovery of lost Star League technology".
According to the BattleCorps story
Proprietary, this rediscovery was in fact made by House Davion, and Capellan agents simply stole double heat sinks from a production facility in Lyran space, skimming them from ongoing production. This was set up on 5 May 3026 and a confirmed delivery of DHS to the CapCon took place in November 3027, implicitly with several previous deliveries. Past actions of BattleMechs that had been equipped with these "parts" were mentioned by late 3027 and "previous similar shipments" in April 3028.
As of early March 3028, House Davion had retrieved one DHS from a salvaged Capellan 'Mech, examined it and traced it to Lyran manufacture.
Summarily, this strongly indicates that the Capellans had access to, and deployed BattleMechs with, FedCom-built DHS by 3027 at the latest, possibly since mid-3026.
The BJ-3 appears among WH Imarra forces in the Sic Semper Tyrannis scenario in
BattlePack: Fourth Succession War (pp. 34-36), dated 24 October 3029.
It was also expressly described to have ten double heat sinks which each are three times as bulky as regular heat sinks (p. 36, "Double Heat Sinks").
The BJ-3 having 10 DHS rules out that this could be the same unnamed experimental variant discussed in TRO:3039 (repeated verbatim in TRO:SW), which was under development in the 3030s, and replaced three heat sinks with "freezers" (so apparently mixed SHS and DHS, which was only ever possible with one type of prototype DHS that ultimately proved not feasible for regular use).
The MUL seems to have renamed the BJ-3 as described in
BattlePack: Fourth Succession War the BJ-3X, with an intro date of 3029. However, the story
Proprietary seems to suggest it was already being deployed no later than 3027.
I feel that there was no need to rename the BJ-3. It was a variant using 10 DHS, built initially using a supply of stolen FedCom DHS.
The other, experimental, unit described (the one with 3 "freezers") may have been an evolution of the BJ-3. Given the nature of its DHS, I don't think it could ever have entered line production.