We fix any dimension $d \ge 1$ and consider the space of continuous functions $\Omega = C([0,\infty), R^d)$ endowed with the topology of uniform convergence of compact subsets. $\Omega$ is tacitly equipped with the Wiener measure $P_x$ corresponding to an $R^d$ valued Brownian motion $\omega$ starting in $x\in R^d$. The Gaussian field $\{H_T \omega)\}_{\omega\in\Omega}$ at level $T>0$ then is given by $$H_T (\omega) = \int_0^T \int_{R^d} \kappa (\omega_s-y) B(s,y)dyds,$$ where B is space-time white noise and $\kappa$ is a non-negative mollifier. The renormalized GMC measure corresponding to the field $\{ H_T(\omega)\}_{\omega\in\Omega}$ is given by $$\widehat{\mathscr M}_{\beta,T}(\mathrm d \omega)=\frac 1 {\mathscr Z_{\beta,T}} \exp\bigg\{\beta \mathscr H_T(\omega) - \frac{\beta^2T}{2}(\kappa\star\kappa)(0)\bigg\} \mathbb P_0(\mathrm d \omega)$$ with $\mathscr Z_{\beta,T}$ denoting the total mass. The total mass or partition function is closely related to the solution $u_{\epsilon,t}(x)$ of the (smoothed) multiplicative noise stochastic heat equation $$d u_{\epsilon,t}=\frac{1}{2}\Delta u_{\epsilon,t} d t+\beta\epsilon^{\frac{d-2}{2}}u_{\epsilon,t} d B_{\epsilon,t},\qquad u_{\epsilon,0}=1.$$ The parameter $\beta$, known as the inverse temperature, captures the strength of the noise. In a recent work by Mukherjee, Shamov and Zeitouni, it was shown that, for fixed $t>0$ and for $\beta$ small enough, $u_{\epsilon,t}(0)$ converges as $\epsilon\rightarrow 0$ in distribution to a strictly positive random variable, while for $\beta$ large, it converges in probability to zero. For $\beta$ small we have proved a quenched CLT for the endpoint of $\omega$ under $\widehat{\mathscr M}_{\beta,T}$ and for $\beta$ large enough, we proved that the endpoint is localized in random regions of the space. We also considered $\ell^\infty$ balls around the path $\omega$. For these balls there is no localization under the GMC-measure $\widehat{\mathscr M}_{\beta,T}$ for any value of $\beta$.