I might be a bit late to offer insight to this that hasn't been provided by the other answers, but I suspect there might be something that hasn't been looked upon yet:
Of course I'm in no way an expert to that topic nor could I provide wisdom not available to a greater extend to our first instance of online knowledge with the capital W.... but I'm a wargamer.
As such I spend much time playing games where a great effort has been spend making them pretty realistic. And while "realistic" and "space warefare" isn't anything you'll find today, one can jump into an P-3 Orion and do ASW all by himself, reading MAD and SAD lines.
And while you'll get games where you can hide your submarine below several thermal layers or even below another ship, conceal your torpedoes behind other torpedoes, turn off all your active sensors (and your engines) of your ASW frigate to make it next to impossible for submarines to detect you without active sensors... all games have to cut it somewhere, to make it still possible for an untrained operative (the casual gamer) to grasp how to use that stuff.
All the other answers are probably correct with their assumptions about how utterly impossible it is to hide in a high vacuum where you are the only source of radiation for a couple of megameters. And that you will be done for once you get into the range of their laser guns.
There is at least one try to get something like active stealth in space, which happens to be the Normandy from Mass Effect, which is said to store their heat internally but need to release it from time to time in an atmosphere... But that seems to be no option when your enemy is expecting you.
So you need to either skip that and just claim that its done somehow for the sake of playability. Even Dangerous Waters, which is a game made from guys that do actually create military grade naval sensors, cuts its realism at one point, which is the way the ocean does work. There are thermal layers in that game, but they do work way more simple than in reality. Or your sonar buoys are limited to shallow and deep, instead of a self defined depth.
And what can you do?
Your game needs to skip that part, where your poor fighter crafts get toasted by lasers, and just insert them right into operational range, either by elaborate handwaving or other means. Still... even if you just plain avert this, there is another problem you need to avert, too: the high speed of objects passing each other in space.
I suggest grabbing the Demo of Kerbal Space Program and try to dock two spacecrafts, which both have a relative velocity of 500m/s. Or just watch it zip past you. It will shift from dot to highly visible to dot in a couple of seconds... and because KSP is scaled down, use km/s instead of for the relative velocities in use by our modern day spacecrafts. If you want to reach your enemy in a decent timeframe, you need to get even faster, where you might get to a point where your timeframe for aiming and shooting is about 10ms.
But why is that a problem? Because your "realistic fighters" would drift out of the "too close to aim" area in a matter of eye blinks. Right into the "absurd big core firing area of any useful laser cannon", which will get a superb trajectory of your fighters zipping by and just need to lead their aim.
To be honest, I did ponder about the mechanics of a realistic space ship fighting game some time ago too, and I needed to forfeit at the point where I didn't found a way to keep the game realistic and playable, because at a given point its duked out not by pilots or weapons, but the Sensor-ECM-ECCM complex.
I noticed that any spacefight would work like this:
- detecting each other (minutes to hours)
- getting into effective firing range (probably even longer)
- being the first to get a weapon lock (micro to nano seconds)
- wait for the laser to hit (a second or so)
And most of the "action" happens in 1 and 3. While 1 can be interesting if you allow some less than realistic approaches to hide and sensor something, 3 will evolve into something that isn't short in tactical depth to chess.
As the others told you, there are way to much emissions to hide from passive sensors, but you might be able to go the other way:
hide in your own blob of em-emissions, or extend it to make your ship a bigger target (and leave the question "where in that 1km² sensor blob is that darn enemy?" up to your enemy). If you can't hide yourself, all you can do is making it as hard as possible to actually get the... exact location of the signatures source.
While that might work if you doing an Star Trek like battle between precise but quite small fleets (or even single ships), an environment with fighters would went for "spray and pray (but with lasers)" to take potshots at as many targets as possible.
Well, that does sound like Battlestar Galactica, but they do use guns for this which are reduced in usefulness to most close range defence (which is sufficient, because its that way there).
Instead of that you could cover that whole 1km² em blob within a second or less using a statistically calculated firing pattern that will grant the biggest chance to hit something with your laser cannon.
So, what can you learn from this?
I would think that you scenario isn't a candidate for "most realistic game of the millenia", so you can...
- drop the fighter/bomber approach,
- avoid the question of "how to ecm them" and start thinking about "what's about the relative velocities",
- try to use the "hide behinde the wall of dead bards" approach, eh, I mean "behind the wall of false sensor information"
- greatly extend the ranges involved to a point where your fighters distribute themselves all over a star system and wait for prey in more usuable location, like the Cronosphere of the local star, at which it would stop feeling like a fighter-carrier game (thats why I didn't even talk about it until now)
I do wonder what you will choose.