diff --git a/outlines/samplers.py b/outlines/samplers.py
index 187318264..393b16af2 100644
--- a/outlines/samplers.py
+++ b/outlines/samplers.py
@@ -96,14 +96,18 @@ def __init__(
         *,
         top_k: Optional[int] = None,
         top_p: Optional[float] = None,
+        temperature: Optional[float] = None,
     ):
         self.samples = samples
 
-        self.logits_processor = lambda x: x
+        self.logits_processors = []
         if top_k is not None:
-            self.logits_processor = keep_top_k_logits(top_k)
+            self.logits_processors.append(keep_top_k_logits(top_k))
         elif top_p is not None:
-            self.logits_processor = keep_top_p_logits(top_p)
+            self.logits_processors.append(keep_top_p_logits(top_p))
+
+        if temperature is not None:
+            self.logits_processors.append(rescale_logits(temperature))
 
     def __call__(
         self,
@@ -132,7 +136,10 @@ def __call__(
         cumulative weights of each sequence of shape ``(n_seqs,)``.
 
         """
-        altered_next_token_logits = self.logits_processor(next_token_logits)
+        altered_next_token_logits = next_token_logits
+        for logit_processor in self.logits_processors:
+            altered_next_token_logits = logit_processor(next_token_logits)
+
         probs = torch.nn.functional.softmax(altered_next_token_logits, dim=-1)
         next_token_ids = torch.multinomial(probs, num_samples=1, generator=rng)
 
@@ -196,6 +203,31 @@ def logits_processor(logits: torch.Tensor) -> torch.Tensor:
     return logits_processor
 
 
+def rescale_logits(temperature: float) -> Callable[[torch.Tensor], torch.Tensor]:
+    """Build a function that rescales the token probabilities exponentially.
+
+    Parameters
+    ----------
+    temperature
+        The value by which we rescale the logits.
+
+    """
+
+    if not isinstance(temperature, float) or temperature < 0.0:
+        raise ValueError(
+            f"`temperature` must be a strictly negative floating point number, got {temperature} instead."
+        )
+    elif temperature == 0.0:
+        raise ValueError(
+            "Please use the greedy sampler instead of setting the temperature to 0."
+        )
+
+    def logits_processor(logits: torch.Tensor) -> torch.Tensor:
+        return logits / temperature
+
+    return logits_processor
+
+
 class BeamSearchSampler:
     """Beam Search sampling algorithm.
 
diff --git a/tests/test_samplers.py b/tests/test_samplers.py
index 3578fcece..88cdb0fbc 100644
--- a/tests/test_samplers.py
+++ b/tests/test_samplers.py
@@ -12,6 +12,7 @@
     keep_top_k_logits,
     keep_top_p_logits,
     multinomial,
+    rescale_logits,
 )
 
 
@@ -72,6 +73,32 @@ def test_multinomial():
     assert weights.equal(torch.tensor([logprobs[0, 0], logprobs[1, 2]]))
 
 
+def test_multinomial_init():
+    sampler = MultinomialSampler()
+    assert sampler.logits_processors == []
+
+    sampler = MultinomialSampler(3)
+    assert sampler.logits_processors == []
+
+    sampler = MultinomialSampler(top_k=1)
+    assert len(sampler.logits_processors) == 1
+
+    sampler = MultinomialSampler(top_p=0.95)
+    assert len(sampler.logits_processors) == 1
+
+    sampler = MultinomialSampler(top_k=1, top_p=0.95)
+    assert len(sampler.logits_processors) == 1
+
+    sampler = MultinomialSampler(temperature=1.0)
+    assert len(sampler.logits_processors) == 1
+
+    sampler = MultinomialSampler(top_k=1, temperature=1.0)
+    assert len(sampler.logits_processors) == 2
+
+    sampler = MultinomialSampler(top_p=0.95, temperature=1.0)
+    assert len(sampler.logits_processors) == 2
+
+
 def test_top_k():
     with pytest.raises(ValueError, match="`k` must be a strictly"):
         keep_top_k_logits(-1)
@@ -159,6 +186,17 @@ def test_top_p():
     )
 
 
+def test_rescale():
+    with pytest.raises(ValueError, match="`temperature` must"):
+        rescale_logits(1)
+
+    with pytest.raises(ValueError, match="`temperature` must"):
+        rescale_logits(-0.1)
+
+    with pytest.raises(ValueError, match="Please use the greedy sampler"):
+        rescale_logits(0.0)
+
+
 def test_beam_search():
     # Two beams, single sequence
     sampler = BeamSearchSampler(2)