The president's public comments have mostly spared Warsh, his handpicked successor to Powell, and focused more on the Fed's other policymakers.
When Powell as chair ignored Trump's various calls to cut rates or not raise them, the president called him an "enemy," a "numb skull" and other epithets.
By contrast last week, Trump characterized Warsh as being boxed in by a "political" board. After the Fed lifted rates for the first time in three years, in a unanimous vote, Trump said that he had told Warsh in a phone call beforehand to go along with the majority if necessary.
Warsh has said he won't discuss conversations with Trump.
Long considered an inflation hawk, Warsh had weeks ago laid out the case for higher rates, surprising some analysts who had questioned his independence from Trump.
Warsh "has repeatedly said the Fed will deliver price stability. Wednesday’s rate hike shows that he means it," Apollo Global Chief Economist Torsten Slok said after the Fed's Sept. 16 decision.
The relative leeway Trump is giving Warsh may reflect their warmer ties early in the new Fed chief's term.
Trump started chiding Powell early in his first presidency for raising rates, and the relationship remained tense. Powell did not openly push back against the rhetoric until early this year, when the administration sent a grand jury subpoena over the construction project.
Warsh appears to have a more congenial relationship, fielding the president's phone calls while maintaining he'll remain an independent broker when it comes to monetary policy.
That policy now includes a hardening stance against inflation.
Polls show that pocketbook issues including record diesel fuel prices are hitting red state rural economies and small businesses, and that Trump's record-low approval rating is dragging down Republican congressional candidates.
A Reuters/IPSOS poll published Monday showed just 17% of respondents approve of the president's handling of the cost-of-living, the top issue Americans say will influence how they vote in six weeks.