This is a question that would be better handled by the experts at Seasoned Advice (I suspect it would be a duplicate.)
Their food safety tag description is a fantastic resource that I commonly refer to, correcting a number of myths and misconceptions. From there, we can see the answer to this question is not a simple "yes or no" - heating them once to a certain temperature doesn't render them safe.
Bacteria leave behind harmful protein toxins that cannot be "killed" (denatured) by cooking. The cooking times/temperatures are only effective against live organisms, not their toxic waste products. Spoiled food cannot be cooked back to safety and must be discarded.
Cooking is pasteurization, not sterilization. Pasteurization means killing most microbes, so as to render the food safe for human consumption. This resets the clock but does not stop it; cooked food can and will still spoil after 2 hours in the danger zone. Sterilization methods (e.g. high-pressure canning and irradiation) are the only safe methods for longer-term room-temperature storage.
Egg safety is a regional issue, with eggs being stored (in production) at different temperatures and use different Salmonella control regimes.
The US government do recommend heating eggnog until it reaches "an internal temperature of 160 °F" (71 °C) to protect against infection.
This paper shows that 40°C for 2 hr or 48°C for 30 min was not enough to eliminate Salmonella enteritidis.
This paper discusses different treatments:
The US Department of Agriculture set-up pasteurisation standards for egg products that any Salmonella
species in the egg is reduced by an amount equal to at
least 5 logs. At present, LWE [Liquid Whole Egg] is
pasteurised at a minimum of 60 °C for 3.5 min to
ensure microbiological safety. In the UK, the regulatory
requirement for LWE is 64 °C for 2.5 min.
They heated egg to 55°C and 60°C for 3.5 minutes, and did not hit these targets.