diff --git a/src/pip/_internal/build_env.py b/src/pip/_internal/build_env.py
index cdf04324107..92f50f750c2 100644
--- a/src/pip/_internal/build_env.py
+++ b/src/pip/_internal/build_env.py
@@ -70,9 +70,11 @@ class BuildEnvironment:
 
     def __init__(self):
         # type: () -> None
+
         temp_dir = TempDirectory(
             kind=tempdir_kinds.BUILD_ENV, globally_managed=True
         )
+        self._sub_temp_dir = temp_dir.make_sub_temp_dir()
 
         self._prefixes = OrderedDict(
             (name, _Prefix(os.path.join(temp_dir.path, name)))
@@ -126,7 +128,7 @@ def __enter__(self):
         # type: () -> None
         self._save_env = {
             name: os.environ.get(name, None)
-            for name in ('PATH', 'PYTHONNOUSERSITE', 'PYTHONPATH')
+            for name in ('PATH', 'PYTHONNOUSERSITE', 'PYTHONPATH', 'TMPDIR')
         }
 
         path = self._bin_dirs[:]
@@ -140,6 +142,7 @@ def __enter__(self):
             'PATH': os.pathsep.join(path),
             'PYTHONNOUSERSITE': '1',
             'PYTHONPATH': os.pathsep.join(pythonpath),
+            'TMPDIR': self._sub_temp_dir
         })
 
     def __exit__(
@@ -202,6 +205,7 @@ def install_requirements(
                 requirements,
                 prefix,
                 message,
+                self._sub_temp_dir,
             )
 
     @staticmethod
@@ -211,6 +215,7 @@ def _install_requirements(
         requirements: Iterable[str],
         prefix: _Prefix,
         message: str,
+        sub_temp_dir: str,
     ) -> None:
         args = [
             sys.executable, pip_runnable, 'install',
@@ -243,6 +248,9 @@ def _install_requirements(
         args.append('--')
         args.extend(requirements)
         extra_environ = {"_PIP_STANDALONE_CERT": where()}
+        if sub_temp_dir:
+            extra_environ["TMPDIR"] = sub_temp_dir
+
         with open_spinner(message) as spinner:
             call_subprocess(args, spinner=spinner, extra_environ=extra_environ)
 
diff --git a/src/pip/_internal/operations/build/metadata_legacy.py b/src/pip/_internal/operations/build/metadata_legacy.py
index f46538a07f4..51b7d69b650 100644
--- a/src/pip/_internal/operations/build/metadata_legacy.py
+++ b/src/pip/_internal/operations/build/metadata_legacy.py
@@ -53,9 +53,10 @@ def generate_metadata(
         setup_py_path, details,
     )
 
-    egg_info_dir = TempDirectory(
+    tmp_dir = TempDirectory(
         kind="pip-egg-info", globally_managed=True
-    ).path
+    )
+    egg_info_dir = tmp_dir.path
 
     args = make_setuptools_egg_info_args(
         setup_py_path,
@@ -67,6 +68,7 @@ def generate_metadata(
         call_subprocess(
             args,
             cwd=source_dir,
+            extra_environ=dict(TMPDIR=tmp_dir.make_sub_temp_dir()),
             command_desc='python setup.py egg_info',
         )
 
diff --git a/src/pip/_internal/operations/build/wheel_legacy.py b/src/pip/_internal/operations/build/wheel_legacy.py
index 755c3bc83a2..7a9404c870a 100644
--- a/src/pip/_internal/operations/build/wheel_legacy.py
+++ b/src/pip/_internal/operations/build/wheel_legacy.py
@@ -9,6 +9,7 @@
     call_subprocess,
     format_command_args,
 )
+from pip._internal.utils.temp_dir import TempDirectory
 
 logger = logging.getLogger(__name__)
 
@@ -70,13 +71,14 @@ def build_wheel_legacy(
     source_dir,  # type: str
     global_options,  # type: List[str]
     build_options,  # type: List[str]
-    tempd,  # type: str
+    temp_dir,  # type: TempDirectory
 ):
     # type: (...) -> Optional[str]
     """Build one unpacked package using the "legacy" build process.
 
     Returns path to wheel if successfully built. Otherwise, returns None.
     """
+    tempd = temp_dir.path
     wheel_args = make_setuptools_bdist_wheel_args(
         setup_py_path,
         global_options=global_options,
@@ -92,6 +94,7 @@ def build_wheel_legacy(
             output = call_subprocess(
                 wheel_args,
                 cwd=source_dir,
+                extra_environ=dict(TMPDIR=temp_dir.make_sub_temp_dir()),
                 spinner=spinner,
             )
         except Exception:
diff --git a/src/pip/_internal/utils/temp_dir.py b/src/pip/_internal/utils/temp_dir.py
index 477cbe6b1aa..c737866f1f7 100644
--- a/src/pip/_internal/utils/temp_dir.py
+++ b/src/pip/_internal/utils/temp_dir.py
@@ -1,6 +1,7 @@
 import errno
 import itertools
 import logging
+import os
 import os.path
 import tempfile
 from contextlib import ExitStack, contextmanager
@@ -12,6 +13,7 @@
 
 _T = TypeVar("_T", bound="TempDirectory")
 
+tmpdir_serial = 0
 
 # Kinds of temporary directories. Only needed for ones that are
 # globally-managed.
@@ -171,6 +173,17 @@ def _create(self, kind):
         # symlinked to another directory.  This tends to confuse build
         # scripts, so we canonicalize the path by traversing potential
         # symlinks here.
+
+        if "SOURCE_DATE_EPOCH" in os.environ:
+            global tmpdir_serial
+            path = os.path.join(
+                tempfile.gettempdir(),
+                "pip-{}-{}".format(kind, tmpdir_serial)
+            )
+            tmpdir_serial += 1
+            os.mkdir(path)
+            return path
+
         path = os.path.realpath(tempfile.mkdtemp(prefix=f"pip-{kind}-"))
         logger.debug("Created temporary directory: %s", path)
         return path
@@ -183,6 +196,14 @@ def cleanup(self):
             return
         rmtree(self._path)
 
+    def make_sub_temp_dir(self):
+        if "SOURCE_DATE_EPOCH" not in os.environ:
+            return None
+
+        ret = os.path.join(self._path, 'tmp')
+        os.mkdir(ret)
+        return ret
+
 
 class AdjacentTempDirectory(TempDirectory):
     """Helper class that creates a temporary directory adjacent to a real one.
diff --git a/src/pip/_internal/wheel_builder.py b/src/pip/_internal/wheel_builder.py
index 92f172bca16..0df0cd8812f 100644
--- a/src/pip/_internal/wheel_builder.py
+++ b/src/pip/_internal/wheel_builder.py
@@ -265,7 +265,7 @@ def _build_one_inside_env(
                 source_dir=req.unpacked_source_directory,
                 global_options=global_options,
                 build_options=build_options,
-                tempd=temp_dir.path,
+                temp_dir=temp_dir,
             )
 
         if wheel_path is not None: