You don't mention the kind of tile or particulars of your basement. So, I'll describe our space and what we have noticed.

We have a conventional basement in the upper Midwest. Concrete floor is below the frost line.

Installed vinyl tile as flooring of the finished portion. There is a perceptible warmer temperature as compared to the bare concrete - enough that visitors often are comfortable without shoes.

Ours is a better grade of "sticky back" tile but was installed with mastic to make certain any unevenness of the concrete would not cause those hollow sounds when walking upon the flooring. Has been in place for around 8 years.

I suspect ceramic tile would transmit the concrete temperature so stand on the existing floor and determine if it's OK.

I've had stone and tile in a few basements. The stone was warmer to the touch than tile and stone tile. Polished marble in the baths was icy to bare feet regardless of the season.