This is the 90th most frequent Czech word.
téměř
Almost.
In this context, 'téměř' is used to mean 'almost'. It restricts the frequency term 'every day' to indicate an event that occurs on most days but not necessarily all.
Téměř každý den chodím na procházku.
Almost every day, I go for a walk.
Here, 'téměř' describes the temperature of the food, indicating it was close to being cold but not entirely so.
Jídlo bylo téměř studené, když jsme začali jíst.
The food was almost cold when we started eating.
In this sentence, 'téměř' qualifies the state of completion, suggesting the task is nearly finished.