March and April represent the hot season, and hot it is — 35°C (95°F) on average, but don't be surprised to see temperatures rising towards 40 degrees Celsius (around 100°F+). This is the worst season to visit Bangkok, so plan a lot of air-conditioned shopping mall visits and get a hotel with a swimming pool.
Then there's the wet season that runs from May till October. Expect massive downpours resulting in floods all over the city, and spells of thunder at times. It's not all bad though — the afternoon showers are actually a pleasant way to cool down from the heat, and while they may last all day, usually they're over within an hour. Extreme rainfall happens in September and October, so these months are best avoided.
Whatever season you're visiting, don't take the weather lightly — temple-tramping in the scorching afternoon sun can be a challenge, so come well-prepared. Dress lightly for the weather, but keep in mind that some palaces and all temples (notably the Grand Palace) have a strict dress code. Also be sure, and this cannot be said enough, drink enough fluids! You don't have a reason not to, as 7-Elevens and other convenience stores are abundant in Thailand and they sell cooled beverages for as little as 10 baht. Locals get their water from "reverse osmosis" purified water machines that fill up a one litre bottle for one baht.