The club also optioned right-hander Brian Omogrosso to Triple-A after throwing 60 pitches in two days. He was 0-1 with a 5.14 ERA in 11 relief appearances after being recalled on May 1.
"Well, without those two new guys, we were going to be very short in case something happened to [Thursday starter Jose] Quintana very early," interim manager Mark Parent said. "We'll be all right. Obviously, we need a good outing out of Quintana."
Peavy has gone 6-4 with a 4.30 ERA this year, with 66 strikeouts in 11 starts. He left with the rib injury after 2 1/3 innings of his start on Tuesday in Seattle.
Troncoso is 1-1 with a 2.19 ERA with eight saves in 21 appearances with Charlotte. He made 175 appearances (all in relief) over parts of four Major League seasons with the Dodgers from 2008-11, going 8-8 with a 3.92 ERA and six saves.
Heath is 1-0 with a 2.25 ERA in 10 outings for Charlotte, and he has a 11.12 ERA in four relief appearances over two stints with Chicago.
Both Heath and Troncoso were available on Thursday, but White Sox closer Addison Reed wasn't after throwing 55 pitches over three innings on Wednesday.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. Ethan Asofsky is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.