Heat kernel on quaternion Heisenberg group

For the n Heisenberg($$\Bbb C^n\times\Bbb R$$) it is known that the heat kernel $$q_s(z,t)=c_n\int_{\Bbb R} e^{-i\lambda t}\Big( \frac{\lambda}{\sinh(\lambda s)}\Big)^n e^{-\frac{\lambda|z|^2\coth(\lambda s)}{4}}d\lambda$$ satisfied the followin estimate: $$q_s(z,t)\leq C s^{-n-1} e^{\frac{A}{s}|(z,t)|^{1/2}}$$ with some positive constants $$C$$ and $$A$$ and $$(z,t)\in \Bbb C^n\times\Bbb R$$ with $$|(z,t)|=(|z|^4+|t|^2)^{\frac{1}{4}}$$.

Now for the one quaternion Heisenberg it is known that the heat kernel $$p_s(x,t)=c\int_{\Bbb R^3} e^{-i\lambda .t}\Big( \frac{|\lambda|}{\sinh(|\lambda| s)}\Big)^2 e^{-\frac{ |\lambda||x|^2\coth(|\lambda| s)}{4}}d\lambda$$ where $$(x,t)\in Q\times \Bbb R^3$$ and $$Q$$ the set of quaternions.

My question can we have the same estimate for $$p_s(x,t)$$. Thank you in adavance