Why not use custom metrics from Prometheus with influxdb-exporter? I don't see why it should not work.

It is possible to use influxdb with heapster, in attachments some files that I set up to use in an easy way.
First run influxdb.yaml
Run second heapster-rbac.yaml
Third run heapster.yaml

**INFLUXDB.YAML**

    apiVersion: extensions/v1beta1
    kind: Deployment
    metadata:
      name: monitoring-influxdb
      namespace: kube-system
    spec:
      replicas: 1
      template:
        metadata:
          labels:
            task: monitoring
            k8s-app: influxdb
        spec:
          containers:
          - name: influxdb
            image: k8s.gcr.io/heapster-influxdb-amd64:v1.5.2
            volumeMounts:
            - mountPath: /data
              name: influxdb-storage
          volumes:
          - name: influxdb-storage
            emptyDir: {}
    ---
    apiVersion: v1
    kind: Service
    metadata:
      labels:
        task: monitoring
        # If you are NOT using this as an addon, you should comment out this line.
        kubernetes.io/cluster-service: 'true'
        kubernetes.io/name: monitoring-influxdb
      name: monitoring-influxdb
      namespace: kube-system
    spec:
      ports:
      - port: 8086
        targetPort: 8086
      selector:
        k8s-app: influxdb

**heapster-rbac.yaml**

    kind: ClusterRoleBinding
    apiVersion: rbac.authorization.k8s.io/v1beta1
    metadata:
      name: heapster
    roleRef:
      apiGroup: rbac.authorization.k8s.io
      kind: ClusterRole
      name: cluster-admin
    subjects:
    - kind: ServiceAccount
      name: heapster
      namespace: kube-system

**heapster.yaml**

    apiVersion: v1
    kind: ServiceAccount
    metadata:
      name: heapster
      namespace: kube-system
    ---
    apiVersion: extensions/v1beta1
    kind: Deployment
    metadata:
      name: heapster
      namespace: kube-system
    spec:
      replicas: 1
      template:
        metadata:
          labels:
            task: monitoring
            k8s-app: heapster
        spec:
          serviceAccountName: heapster
          containers:
          - name: heapster
            image: k8s.gcr.io/heapster-amd64:v1.5.4
            imagePullPolicy: IfNotPresent
            command:
            - /heapster
            - --source=kubernetes:https://kubernetes.default?kubeletHttps=true&kubeletPort=10250&insecure=true
            - --sink=influxdb:http://monitoring-influxdb.kube-system.svc:8086
    ---
    apiVersion: v1
    kind: Service
    metadata:
      labels:
        task: monitoring
        # If you are NOT using this as an addon, you should comment out this line.
        kubernetes.io/cluster-service: 'true'
        kubernetes.io/name: Heapster
      name: heapster
      namespace: kube-system
    spec:
      ports:
      - port: 80
        targetPort: 8082
      selector:
        k8s-app: heapster

InfluxDB can be used with Heapster(as pointed out by @LucasSales) but it is deprecated in the current versions of Kubernetes.
For the latest versions of Kubernetes we have the metrics server for basic CPU/memory metrics. Prometheus is the accepted third party monitoring tool especially for things like custom metrics.