John Murray says he is reconsidering his company's 5000 pitchside sponsorship at Tynecastle
Plumbing firm Paragon Trade Services Ltd, which said it was set to unveil five adverts around the stadium, would follow MacB Water which yesterday announced it was ending its deal as water sponsor of the team over the affair.
It came as parents today branded the club "disgusting" after a primary school was forced to cancel a trip to the Hearts training ground amid fears Thomson would be there.
Hearts suspend sex shame star Thomson
John Murray, director of Paragon, told the Evening News: "I have been a Hearts supporter my whole life but the reputation of the club has been tarnished by this.
"I'm a family guy and don't agree with what's going on, so I'm considering pulling the plug on my advertising."
Mr Murray's business is thought to be worth around 5000 to the club, a similar amount to the MacB contract.
Meanwhile, a spokesman for shirt sponsor Wonga reportedly said its two-year deal would continue while strip supplier Umbro has asked the club to keep it informed about the situation.
Defender Thomson, 20, was fined and placed on the sex offenders register in relation to his inappropriate conduct towards two underage girls over the internet. Last week, Hearts told him he could stay following a club investigation into his conviction for "lewd, libidinous and indecent behaviour".
Today, an alleged victim of Thomson reportedly claimed he had targeted dozens more underage girls online, sending them lewd messages.
Two classes of pupils aged six and seven were due to train with Hearts players at Riccarton yesterday, but Pentland Primary pulled out of the visit at the last minute.
Parents were angry the children had to miss out, but backed the Oxgangs school's decision.
Initial fears were that Thomson was at the training ground, having remained in the city while the rest of the squad headed to Italy, although Hearts later denied this claim.
One mother, who has a girl in one of the primary two classes due to visit the facility, said: "We've all paid for the trip and the coaches were there this morning and the children had all turned up in their tracksuits.
"We were left with two P2 classes of six and seven-year-olds breaking their hearts in the school with no trip to go on because of him.
"The class teacher said it was cancelled for health and safety reasons because Thomson was in the training ground."It's disgusting."
Heather Levy, whose daughter went on the same trip a few weeks ago, said: "The school has a responsibility to provide a safe environment for children and I think they did the right thing.
"Children are so vulnerable and parents are entrusting the school to be sure that they are going to be safe."
A council spokesman confirmed that Pentland Primary cancelled the trip and said that the authority supported its decision.
A spokesman for Hearts said he was not contacted by the school to discuss cancelling the trip and said Thomson was not at Riccarton yesterday.