Asked of Hamilton's condition, Elliott said: "I saw him about an hour after that and he was definitely a chunk better and I know he has recovered since then.
"I think if you have never been near these cars, it is really difficult to understand the environment the drivers are in.
"The air that is going by the car, actually because the car is so close to the ground, it is actually closer to the ground temperature than it is to the air temperature.
"So, during that race, I suspect that was sort of 40, 50-degree air, it was humid, the drivers are also sitting in an environment where there are electrical boxes around him, hydraulics with power steering, a hot environment and that was one tough race."
Hamilton struggles "unsurprising" in Hungarian heat
The heat at the Hungaroring was sweltering all weekend even with the rain shower that hit the circuit at the beginning of the race.
Hamilton was forced to fight back from a Mercedes strategy error and Elliott suggested this had a part to play in the health concern.
"Lewis was really pushing on that two-stop, some of the overtakes he was doing were absolutely brilliant," he added.
"That takes a lot of energy out of you in that really hot environment. The average person like you and me, we wouldn’t survive five minutes in there, let alone a whole race.
"So, it was unsurprising that Lewis was tired at the end of that, but as he said to the media I think he also wonders whether that is some of the feeling of having had Covid.
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