[1] He won his first Olympic gold medal by swimming the lead-off leg in the men's 4×200-meter freestyle relay, and Heath and his American teammates David Larson, Jeff Float and Bruce Hayes set a new world record of 7:15.69, edging the Michael Gross-led West Germans by four one-hundredths (0.04) of a second.

[12][13][14] He won his second gold medal by helping set another world record of 3:19.03 in the men's 4×100-meter freestyle relay, together with fellow Americans Chris Cavanaugh, Matt Biondi and Rowdy Gaines, finishing sixty-five one-hundredths (0.65) of a second ahead of the second-place Australians.

[1] In a word play on the title of the popular 1984 movie Ghostbusters, American media dubbed Heath and his 4×200-meter relay teammates the "Gross Busters.

"[16][17] In individual Olympic competition, Heath won a silver medal in the 200-meter freestyle (1:49.10) behind Gross's world record-setting performance (1:47.44).

[18] He also placed fourth in the 100-meter freestyle event final (50.41); the outcome was controversial, however, because of a premature starter gun and a quick start by Gaines, the winner.

At the 1985 Pan Pacific Championships in Tokyo, gold medalists Scott McCadam, Heath, Paul Wallace and Biondi set a new world record of 3:17.08 in the 4×100-meter freestyle relay.

Individually, Heath won a Pan Pacific Championships gold medal in the 200-meter freestyle (1:49.29) by beating Biondi (1:50.19) and Canadian Sandy Goss (1:50.56).