No. To be honest, I was a bit baffled by your question: why would you think that it would take the same time to heat as to cool?
It will heat depending on how quickly you can get energy to it, and it will cool depending on how quickly you can remove energy from it. Have you never seen an electric heater or oven and noticed they heat quickly and take a while to cool down? Or rapidly cooled something by putting it in iced water or a freezer?
There's nothing to be baffled about, it's a fair question. You even provided the answer: "It will heat depending on how quickly you can get energy to it, and it will cool depending on how quickly you can remove energy from it."
On the other hand, there's no "electric heater" here to use to heat up the liquid used to absorb solar heat (not to mention ice or freezers...); it's the sun or nothing. Given that the sun doesn't give us peak solar flux until the midday it's entirely possible that solar energy production in the first few hours of the day would only keep up with instantaneous energy needs instead of having enough of an excess to reheat the heat storage fluid for energy production later that night.
Whether this is actually an issue or not depends on the numbers, but it's not a baffling question at all and there's no reason to be so condescending about it.
It's baffling to me because it makes no sense based on everyday experience to think that things have a set amount of time that they heat up or cool down. Why would anyone think that?
If you think my comment was condescending, stop reading it in a condescending tone.
It will heat depending on how quickly you can get energy to it, and it will cool depending on how quickly you can remove energy from it. Have you never seen an electric heater or oven and noticed they heat quickly and take a while to cool down? Or rapidly cooled something by putting it in iced water or a freezer?