The former British prime minister was named in connection with inquiries carried out by detectives in London, Kent, and Jersey.
On Monday, Wiltshire Police appealed for potential victims and witnesses to come forward.
Reports subsequently emerged that Heath is being looked at as part of Operation Midland, a Scotland Yard inquiry into claims that a VIP paedophile ring operated in the 1970s and 1980s.
The Metropolitan Police woul not confirm the claims. A spokesman said: “We are not giving a running commentary on Operation Midland.”
Jersey Police confirmed Heath features in Operation Whistle, an inquiry in to alleged historical abuse on the island.
Operation Whistle was launched by police in Jersey in June as part of Operation Hydrant, a UK-wide co-ordination of sex abuse probes.
Later, Kent Police said it had received a report of a sexual assault in the east of the county in the 1960s.
A spokesman said: “The victim has named Sir Edward Heath in connection with the allegation. Detectives are making initial inquiries and will obtain a full account from the victim.”
Wiltshire Police said its officers and the NSPCC had received “a number of calls”. It said: “The investigation team will be reviewing the information and following up any lines of inquiry as a result.”
A spokeswoman said they were unable to confirm how many people had made contact and the “validity” of the calls was not yet known They received a mixture of “intelligence” and “third-party” calls, she added.
On Monday, Heath’s name was linked to paedophile claims when the police watchdog announced an inquiry into allegations a prosecution against an individual was shelved after a threat was made to “expose” him.
A woman who was in charge of a brothel had been due to stand trial, but said she would expose him, according to reports. The IPCC is also looking into whether Wiltshire Police followed up a claim made against him in the 1990s. Meanwhile, a man claimed he was raped at aged 12 by the ex-prime minister.
The alleged victim, now in his 60s, has claimed he reported being sexually assaulted by the Conservative MP in 1961 but was branded “a liar and a fantasist”.
Labour MP Tom Watson has claimed he passed information relating to two allegations of abuse involving Heath to police since 2012.
The Sir Edward Heath Charitable Foundation said: “We welcome the investigation by Wiltshire Police, which we wholeheartedly believe will clear Sir Edward’s name and we will co-operate fully with the police in their inquiries.”