My warlock takes the Fiendish Vigor (PHB p.111) invocation, allowing them to cast False Life (PHB p.239) as a first level spell at will.
False Life
1st-level necromancy
Casting Time: 1 action
Range: Self
Components: V, S, M (a small amount of alcohol or distilled spirits)
Duration: 1 hour
Bolstering yourself with a necromantic facsimile of life, you gain 1d4 + 4 temporary hit points for the duration.
My intent was to recast this ability several times between battles until I hit the maximum effect, 8 temporary hit points. However, my DM ruled that my character is unaware of how effective the spell cast was, and can't determine whether a given cast was for 5, 6, 7, or 8 temporary hit points. I went along with it at the time, but I'm wondering if there is any precedent of a character recasting spells to maximize the effect.
Best Answer
"You" get to choose which temporary hit points to keep
The rules for temporary hit points state:
But who is "you"? The player or the character? The Combat chapter (which contains the temp HP rules) switches between the two meanings:
The "you" that attacks with a weapon is arguably both the character and the player. The "you" that rolls damage dice is clearly the player. False life works the same way. The player chooses to cast the spell, the character casts it, the player rolls dice for the spell, and then the player chooses which temporary hit points to keep.
There is precedent for the DM making some rolls for you
The DMG's Running the Game chapter first establishes a baseline:
Later on, it provides one scenario where the DM may choose to roll for the player:
In my experience, certain skill checks are the only time I've ever seen a DM roll dice for a player. I have never seen a DM roll damage (or healing) for a player's spell - and particularly not secretly.
Combining magical effects
I believe that the rules for temporary hit points are more specific than the general rules for combining magical effects. This would mean that you only choose which temp HP to keep each time you cast - you don't simultaneously have 4+ different possible temp HP values. If your DM keeps the old and new temp HP values secret, you won't know which one to choose.
If the temporary hit points from the "most potent" casting of false life simply suppressed the other castings, then what would happen in the following situation:
How many temporary hit points do you now have? Do you suddenly jump up to 5, since the "more potent" casting has ended? Or do the suppressed castings of false life somehow also take the damage? I believe the most straightforward answer is that each casting forces you to make a one-time choice between the old and new value at the time of casting, per the rules for temporary hit points.
Establish expectations
In the end, it's up to your table. However, here are some things to consider when discussing how to proceed: