Good luck getting a definative answer (i will actually disagree with fly and Peter, I don't like the takeout DBL with this hand). This hand illustrates why they preempt: to give you problems.
Your RHO might have anything from a reasonable game try (S-KQT9 H-QT9x D-AK C-QJT) in which case 4S will get cracked, and 4Hx figures to make, to a very weak hand like (S-xxx H-Axx D-Jxx C-xxxx), where you might even make 6S. This means, quite literally, that any of these three bids could be right. The good news is you are only playing for matchpoints, so the most your decision can cost is one full board. :-)
As a side note, with some peoples preempts today you can't even be certain that your partner is short in hearts (although opener likley has 6/7 lately I have seen 3H at this vul on five card suits, and raiser if weak, might have 2. So while I think partner has a heart singleton or void, as many as 3 is not totally out of the question... Especially if the 3H bidder is a certain bulgarian).
Now to what to bid? The odds are that your partner has a little something as RHO will raise with very little on this kind of auction. Assume "normal bridge" if you double (takeout), your partner will be too short to leave the double in. So dbl or bid 4S, and your side is declearing the hand. If your doulbe is "cooperative" after this kind of raise, then that would be great bid for this hand. But for me dbl is takeout.
Since with 3H's if I double, we are declearing the hand anyway, we should remove double as an option. That leaves me with a timid pass and an aggressive 4S.
Advantage of 4S. A) You introduce your suit,

partner is likely to have a few spades (since short in hearts), and if not will have a two long minors and might give you option of five of your better minor, c) takes the pressure off your partner to balance, d) might get you to your only makable game, e) Keeps your partner from bidding 4NT for pick a minor when he is 3-0-5-5.
Advantage of Pass. A) avoids 4Sx down two or more when it is wrong,

avoids 4S down one or two when you are beating 4H, C) allows your partner, who is short in hearts to reopen with dbl which brings both 4S and 4Hx back into the picture.
What would i do? It is close between 4S and pass. But in the final analysis, to make game, your partner will need more than honor or two in spades, and a diamond card. With something like S-Qxx H-x D-Axxx C-xxxxx you will lose at least one trick in each suit, and if you ruff two hearts in dummy, you may lose 2 Spades, so you may have an additional loser.
If you can pass in tempo, that might be the best bid. But I suspect by the time you work through what to do, if you pass (slow pass), your partner would be barred from a light reopening doulbe when he has "the right hand." So I guess I would roll the dice and blantantly bid 4S's, although I respect anyone who backs the decision to passes in tempo, expecting partner to reopen with a takeout double when short in hearts even with only 3 spades (in case you had penalty dbl hand).
Ben