Translation:If he was thirsty, he would drink even water.
I disagree. "If I were" is correct only if you are stipulating a condition contrary to fact. For example, "If I were king" -- but I'm not.
In the sentence here, however, the "if" is not contrary to fact but is rather the equivalent of "when/whenever"-- When he was thirsty, he would drink even water. In this case, "If I was thirsty" is correct, but not "If I were thirsty".
Nowadays many English speakers ignore the subjunctive and say "Ïf I was" all the time and never "If I were". There is therefore a temptation to "hypercorrect" and change every "If I was" to an "If I were". But there are some times when "If I was", and only "If I was", is in fact correct.
You're wrong because the first conditional (more probable) would be "If I am thirsty, I drink", but that does not correspond to this sentence. "By" translates to "would" and "kdyby" translates to "if he were", which are both second conditional forms (less probable). Therefore, the correct translation is "If he were thirsty, he would drink" (second conditional).
In case anyone still cares, here’s what Wikipedia says about this, “The past tense (simple past or past progressive) of the condition clause is historically the past subjunctive. In modern English this is identical to the past indicative, except in the first and third persons singular of the verb be, where the indicative is was and the subjunctive were; was is sometimes used as a colloquialism (were otherwise preferred), although the phrase if I were you is common in colloquial language.”